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Pranjal Pandey
Banaras Hindu University (BHU), Varanasi
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12P/221/31 Question Booklet No ....... l44 ...... . (To be filled up by the candidate by bluel black ball point pen) Roll No. LI_-'----'_...I.._-'----'_...I..I_-'---' Roll No. (Write the digits in words) , . . _...................................................................................... .. Serial No. of Answer Sheet .............................................. . ........................................... Day and Date .................................................................... ( Signature of Invigilator ) INSTRUCTIONS TO CANDIDATES I~: se only blue/black ball-point pen in the space above and on both sides of the Answer Sheet) 1. Within 10 minutes of the issue of the Question Booklet, check the Question Booklet to ensure that it contains all the pages in correct sequence and that no page/question is missing. In case of faulty Question Booklet bring it to the notice of the Superintendent/Invigilators immediately to obtain a fresh Question Booklet. 2. Do not bring any loose paper, written or blank, inside the Examination Hall except the Admit Card without its envelope. 3. A separate Answer Sheet is given. It should not be folded or mutilated. A second Answer Sheet shall not be provided. Only the Answer Sheet will be evaluated. 4. Write your Roll Number and Serial Number of the Answer Sheet by pen in the space provided above. 5. On the front page of the Answer Sheet, write by pen your Roll Number in the space provided at the top, and by darkening the circles at the bottom.. Also, wherever applicable, write the Question Booklet Number and the Set Number in appropriate places. 6. No overwriting is allowed in the entries of Roll No., Question Booklet No. and Set No. (if any) on OMR sheet and also Roll No. and OMR Sheet No. on the Question Booklet. 7. Any change in the aforesaid entries is to be verified by the invigilator, otherwise it will be taken as unfair means. 8. Each question in this Booklet is followed by four alternative answers. For each question, you are to record the cOlTect option on the Answer Sheet by darkening the appropriate circle in the corresponding row of the Answer Sheet, by ball-point pen as mentioned in the guidelines given on the first page of the Answer Sheet. g, For each question, darken only one circle on the Answer Sheet. If you darken more than one circle or darken a circle partially, the answer will be treated as incorrect. 10. :Vote that the answer once filled in ink cannot be changed. If you do not wish to attempt a question, leave all the circles in the corresponding row blank (such question will be awarded zero mark). 11. For rough work, ust': the inner back page of the title cover and the blank page at the end of this Booklet. 12. Deposit only the OMR Answer Sheet at the end of the Test. 13. You arc not permitted to leave the Examination Hall until the end of the Test. 14. If a candidate attempts to use any form of unfair means, he/she shall be liable to such punishment as the University may determine and impose on him/her. [No. of Printed Pages: 54+2 12P/221/31 No. of Questions/"lIV'ii <lit m..n : 150 Full Marks/~ : 450 Time /"ff'fffl : 2 % Hours!'Ef'Jl. Note/m: (1) Attempt as many questions as you can. Each question carries 3 marks. One mark will be deducted for each incorrect answer. Zero mark will be awarded for each unattempted question. ~ -.;8 "" lI'ff'! -.i( 1 ~ m 3 3i<!; "" t 1 ~ 'lffi! 3m if fuv, ~ 3i<!; q;m "ITI('TT 1 ~ ~ m "" lffiliq; 'IF' -;;'t'lT 1 3l\lmf"", w-i\ <i't (2) If more than one alternative answers seem to be approximate to the correct answer, choose the closest one. 'Ili\ 1. 0:-;11<> .. ~ .. P1 .. 3m ~ 3m Mean of n observation is x. If one observation X, then the value of xn+l is n ~~ "" 'If.l "" '!It'! x tl 'Ili\ 1 j; ~1W'T Xn,l ~ xn+l -.<t, <it r.. .. <"q ~ 3m ~ 1 is added, mean continues to remain am;;it. WIT "111(, <it ,j\ '!I"f x ~....., to <it xn'l t (I) 0 2. if f.'t<R (2) (3) n 1 (4) x The first four moments of a distribution about mean are 0, 2, 0 and 11. Then the distribution is (1) leptokurtic (3J (347) (2) platykurtic mesokurtic (4) Nothing can be concluded 1 (P.T.D.) 12P{221{31 (I) ~'1 ~ (3)_~ 3. Variance of first n natural numbers is (I) (3) 4. (n;lf n 2 -1 (4) n (n + 11I2n + I) 6 6 If the geometric mean of positive numbers Xl. X 2. "', X n is G, the geometric mean of 2Xl,22X2, ,2nXn is 1!ft\ ""- """,3if = X"X 2 ,"',X n 'fiT ~ 1.fl'<I G ;iPn n n (2) 22G (I) 2G 5. (3) 2 t, <i\ 2X,,2 2 X 2 , ,2 n X n 'fiT ~ +, 2 G Fifteen candidates appeared in an examination. The marks of the students who passed in the examination are 9,6,7,8,8,9,6,5,4,7. The median of the marks of all the fifteen candidates will be 'P;\l """,ff M ,!!\,", 1\ ~ ~I 9, 6 , 5, 4, 7. '!!'fi 'P;\l 3l"lf$i\ (I) (347) 7 t .n ~ ,!!\,", J!llliq;f </ij (2) 6'5 1\ '3<ftuf 11,1\ ll1fl<!'fiT M . (3) 6 2 ~ >rJHiq; ~ 9, 6, 7, 8, 8, (4) 7 5 12P/221/31 6. If the variance of Yl,Y2,"',YlO 8. 1. 2, "', 10, then variance' of CfiT '5fmUT 10 ~ am: Yi=5xi+4,i=1,2, ,lO, it Yl.Y2, ,YlO CfiT tiMr ml"(U] 7. is 10 and Yi = SX I + 4, 'i = IS ~ xI,x2"",xlO (I) XI_ X2. "', X 10 54 (2) (3) 250 50 (4) 254 Second and third central moments of a distribution are equal. What is the nature of the distribution? (1) Symmetric (2) Asymmetric (3) Positively skewed (4) Negatively skewed (1) wrflrn (2)~ Four years ago, the average age of a family of four persons was 18 years. During this period, a baby was born. Today, if the average age of family is still 18 years, what is the age of baby? (1) 2 0 years "IR _ (I) 9. '!'f '['l ml\ '!fum it; 'lli\ ~ <lit """" ~ 18 '!'f 2ft I '" ,ffi; '!fum <lit """" ~ 18 '!'f ~ t <it fu'lJ <lit ~ 'I'IT i? 20 '!'f (2) -.jfq "'" fu'lJ '!iT """ Ii,an I 25 '!'f In a mesokurtic distribution, the fourth central moment is 243. I,ts standard deviation will be (I) 9 (347) (3) 27 (2) 3 3 (4) 81 (P. T.O.) 12P/221/31 10. A man having to drive 90 km wishes to achieve an average speed ,of 30 lan/hr. For the first half he averages only 20 lan/hr. His average speed in the second half of the journey in order to achieve the desired average should be fom 90 km ~ ~ t, 30 km/hr <f;\ 3i'mi! >ffiI 11TH q;r;rr "'"'"t I <mIT it '"" "'" "'" ~ 3i'mi! >ffiI 20 km/hr ~I <mIT it ~ "'" 1\ ~ ~ 3i'mi! >ffiI lITH .rn it ~ ~ 3i'mi! >ffiI ir.fl 1('" -..fu; (I) 40 km/hr 11. (2) 45 km/hr (4) 60 km/hr The limiting form of a histogram when class intervals are made very small is frequency curve (I) frequency- polygon (2) (3) oglVe (4) pie diagram 'If!; "" """"" ~ m?: (I) 12. (3) 50 km/hr 'I(~I("' ~':!'" (2) 'IR ~ "IT'i, til 'I(~I(", 3!Tlffi ""' (3) m "" ~ l"! oT<n t iffiur (4) ~ m The mean of 50 observations is 40 and s.d. is 8. If 4 is added to each observation, then the new mean and s.d. are (2) mean = 44, s.d. = 12 (I) mean = 40, s.d. = 8 (3) mean = 44, s.d. = (4) mean 8 =40, s.d. = 12 50 ~\l"Il "" l!I"'I 40 i!'l1 l!R'Ii ~ 8 tl 'If!; ..,,)q; ~""" 1\ 4 -.it\< ~ '""', til "'" l!R'Ii ~ WIT (I) 'l1"1 =40, l!R'Ii ~ =8 (3) 13. = 44, l!R'Ii ~ .!. 2 (2) l!I"'I =44, l!R'Ii ~ =12 =8 Let the two regression lines be y between x and y is (I) (347) 'l1"1 'I'!T 'l1"1 (4) 0::: 'l1"1 -2x +3 and 8x (2) _I 3 (3) .!. 3 4 = 40, l!R'Ii ~ = 12 = -y +3. Then correlation coefficient (4) I 2 12P/221/31 14. Let the rank of n individuals be 1, 2, 3, "', n and n, n correlation is (I) 15. 16. .!. (2) I 2 (3) ~ 1, "', 1 respectively. Then the rank. I (4) -I 2 The correlation coefficient between height and intelligence quotient (IQ) of adult persons is generally near to (I) 1 0 (I) 1 0 i\; f.i<R (2) 0'75 (2) 0 75 i\; f.i<R (3) 0'25 (3) 0 25 i\; (4) 0 f.i<R (4) 0 i\; f.i<R What condition should be satisfied for E[y-a-bxj 2 to be minimum? (I) " a=~y boO, (2) a=O, b =-.!51L ,,' x (3) 17. b == xy 2 ' a==lly-bJlx "x Suppose that the regression line of y on x for a set of data has been calculated as y == 5 5 -13 5x. Then which one of the following statements is false? (1) There is a negative correlation between x and y (2) The regression coefficient of x on y would be negative (3) The standard deviations of y and x are equal (4) If (,347) x = 5, then !l = -62 5 (P.T.D.) 12P/221/31 ~ lln "!fIi<i\ iii "-'" WJ"f'I iii ~ x '" y WfTWlUT 1:1m "Oil yo5 5-13 5x. <it f.1",~""d if ,,:t.;-m om! 'TffiI~? 'lH (I) x x "Oil ~ t <fiT ~~ ~ *,U!k4C6 ~ q-( (3) Y "'IT x iii 'lfi; """' y iii ofR ""11,4" "'-" ~ >i1< (2) Y (4) 18. ",oro '1"RT W 'lH<> ~ W!H X 05, "" t Y 0 -62 If for two attributes A and B, the class frequency (AB) ==0, then Yule's coefficient of association Q is equal to (I) I (2) -I (3) 0 (4) any value between 0 and 1 'lfi; i,t"T'l'l'i! A a<tt B iii ~ 'l'f .,("'I\dl (AB)~O, "" 'I." "" ~ ~ Q 'I'J'f(-;i'r'1! 19. {I) I (3) 0 (2) -I If X and Y arc independent variates each with zero mean and unit variance, then the correlation coefficient between (X ---:kY) and (X +Y) will be maximum when k is "'IT Y iii "41"" "PI "d'IT lIffiUT """"'-" :J"Tf"' ~ -;i'r'1! 'lfi; k "" 'lH m 'lfi; ~ (I) 20. 0 'i'R X (2) I (3) -I m, <it (X - k Y) "d'IT (X + Y) (4) -2 In the usual notations, a non-zero value of (l1~x - r2) is associated with (1) linearity of regression of y on x (347) ~ (2) linearity of regression of x on y (3) non-linearity of regression of y on x (4) non-linearity of regression of x on y 6 iii ofR 12P/221/31 lI1llT"l ~ ~i),., ( I) Y 21. <I:t x '" ..l if (~~x _r2) "" 1P' II ~ x <I:t y '" W!T&ll"T <I:t hlIl'ffll (3) Y (4) x <I:t y '" W!T&ll"T <I:t W!T&ll"T <I:t ;mcll"., aitoii"., For 3 attributes, the number of ultimate class frequencies is (I) 9 22. <I:t hlIl'ffll W!T&ll"T (2) <I:t x '" l!R ~ ~ (2) (4) 10 (3) 8 6 Given (AB) ~ 256,(aB) ~ 768, (A~) ~ 48,(a~) of the following statements is true? ~ 144 for two attributes A and B, which one (1) The data is consistent (2J The data is not consistent (3) A and B are independent (4) A and B are negatively associated W :rm f.i",r~r,," (I) (3) 23. i\; ~ ~ ~ % lAB) ~ 256, (aB) ~768, (A~) ~ 48, (a~) ~ 144, if II -.i'R-m (2) A "" B f';mil Be A (2) ~ if (4) A "'" B For two events A and B with Be A, if (1) 0 <it '<'I'! "ffi'! ~? ~ if ~'""'''' ~ A "'" B ""'" ~ w"""oil (347) A 11m B 7 ~ ""II,q .. ~ ~ 2 (3) 2 if '!tl P(A)~~ and PIB)~~, then t ~ P(A)=~2 ~ ~,q",,,, "" ~ 4 4 PIB)=~, <it 4 P(B/A) is P(B/A)-.Pft (4) 1 (P.TD.) 12P/221/31 24. In usual, notations, which one of the following is true? (I) PIA) ~ P(A)+P(B) ~ P(AuB) ~ P(AnB) (2) P(AnB)~P(A)~P(A)+P(B)~P(AuB) (3) P(AnB)~P(A)~P(AuB)~P(A)+P(B) (4) None of the above ""'"" -.iiI;,rr.,ro ii, f.l .... P"fuI" iI it t, (I) P(A)~P(A)+P(B)~P(AuB)~P(AnB) (2) P(AnB)~P(A)~P(A)+P(B)~P(AuB) (3) P(AnB)~P(A)~P(AuB)~P(A)+P(B) (4) ~ 25. ~-m "'" if it q,'\{ ~ Which of the following pairs of events is mutually exclusive in toss of four c9ins? (1) At least two heads and utmost two tails (2) At least two heads and at least two tails (3) At least three heads and utmost three tails (4) At least three heads and at least three tails 'ITl fln>'f '!it ~ ( I) q;q -it -q;q wm iI it ~-m 'Rrn ~ t, 1(\ -.M a1t< 3lfll<!; -it -3lfll<!; 1(\ T"" (2) q;q -it - q;q 1(\ {347) if f.l .... P"fuI" '1G'!T'l1l t -.M a1t< q;q -it - - 1(\ T"" (3) q;q-it-_ <fr.! -.M a1t< ,m'"",-it-3lfll<!; <fr.! T"" (4) q;q -it -q;q <fr.! -.M a1t< _ -it -q;q <fr.! T"" 8 12P/221/31 26. The probability of two persons being born on the same day is 1 (1)-- 2) 1 I 365 49 27. (3) 1 (4) 7 ~ 7 An unbiased coin with faces marked 1 and 2 is tossed two times. Let X be the number obtained in the first toss and'Y be the maximum of the two numbers obtained. Then PIXoYjis "'" ""If_ fu1!i1, ~ ~ '" 1 "'IT 2 fu1m t, <;1 om :mR!T "fl<!T t I 'IF! ~ X ~"" ~if ]!ffi <i&n "'IT Y <;1ij 3i<IB1 if ]!ffi <i&n if ~ t I <it PIX ~ Y j '!iT 'IF! tiPn (I) ~ (2) 4 28. ~ (3) 2 ~ (4) 4 1 If three small squares are chosen at random on a sixty-four square (chess) board, the chance that they are in a diagonal line is 'lfi.; <i\m "'" qffi (~) ~ 00 if ~, """ -.nt B "'<;RI" "ill", mz "'" '!iT """ lln'lT .wi, <it "" "'" 1iMt (2) 6/744 II) 5/744 29. I ~ B <fH (3) 7/744 (4) 8/744 (3) ~2 (4) ,,2 If random variable X takes values <IT?: <OJ I ~f.i~<fl ~ X 'IF! """ ~ X ~+" ~-" PIX) 1 2 1 2 then coefficient of kurtosis P2 is <it~~P2 ( I) (347) 0 t (2) 1 9 (P. T. D.) 12P/22J/31 30. Let x be a continuous random variable with distribution function F x (.)' Define Z = Fx{x). Then var {Z 1 is l!HT x '"" WI<! ., ~r;;,,'h (I) 31. ! "i'f{ (2) 2 t PI-P2 1- P3 (2) l!HT Z ~ F x ( x)1 ~ 13 <it (Z) 'hi >ml"T (4) I (4) P2 - P3 1- PI -.'\'11 am P (AB) ~ P3 I <it P (B/A) Wfi PI - P3 I-P2 'l" ij '"" ~ Ol~r;;,,'h ~ '!ftfu it, Wfi (I) ! (2) 2 it fu'I1 ~ "lilI'h"1 ill; "" ~ ~ '1'111 ! (3) ! 4 3 (4) it wftq -.'\'11 " ill; ! 5 Let X be a random variable with.c.d.f. F(x)=l_e-J..x, O<x<oo, Then EIXjis l!HT ill; 01 ~Rll'h "i'f{ X 'hi <i'l'fi oir-! 'li<'R F (x) ~ 1 - e- '" , 0 < x < 00 (2) l. (I) 21. (3) Let variate X have the distribution PIX ! l. t I <it E I X J -.'\'11 (4) ~OJ~PIX ~2J~p; =::; .!..2 Then for what value of p, var (X) will be maximum? l!HT ill; "i'f{ X 'hi 0.-:;; p iii flRI (I) 0 (347) (3) 12 tI A point is selected at random in a circle. The probability that the point is closer to the centre than to its circumference is ilf;>f\ 34. 'li<'R F x (0) Let P(A)~PI,P(B)~P2 and P(AB)~P3. Then P(B/A) is (I) 33. oir-! ~ l!HT ill; P (A) ~ PI, P (B) ~ P2 32. f.mq;, l!H iii #ro: ?:. 2 PIX ~IJ~I-2p for oir-! t P I X ~ 0 J ~ PI X ~ 2 J ~ p; P I X ~ 1 J ~ 1- 2p; 0 ~ P ~! iii #ro:1 <it P 2 (X) 'hi >ml"T ~ (2) -.'\'11? ! (3) 4 10 1 (4) ! 2 12P/221/31 35. The cumulative distribution function of any random variable is 1. always right continuous II. right discontinuous at countable number of points III. monotone non-decreasing Select the correct answer from the following : (l) None of the above three statements is always true (2) I and III are true, but II is false (3) U and III are true, but I is false (4) All the above three statements are true when the M ",~o; '" 'fiT ~ m '1iffi I. >$" ~ ""'L II. ~ ~ qffi ~3il 'R ~ f.i '" lie fig rl ~ " >It\ OW to "'IT t [31 II !II "'" *""\ ~ 'ltl ~ ~ II 3ffiF! ~ ~ I 3ffiF! ~ [41 m)m"$if ""l'! "'" ~ ~ .,~o; '" 36. *""\ ~ let X, Y, Z be i.i.d. continuous variates. Then PIX > YjY > Z mT [II Ri X, Y, Z ~ 3 {3471 is discrete ;jRrr ~ [ I I m)m"$if q;,ffi ~ " ~ 1i\ >$" "'" [21 I <I'll III "'" LV. Wffi " ~ [2) m qffi ""'L '" ~ il <IT PIX> Y/Y > Z (3) 2 3 2 11 1is [-.Pi! (4) I (P.T.D.) 12P/221/31 37. The joint p.d.L of IX, Y} is IX, Y) '!iT ~ <If.<''"f ""'" ~ fix, y) ~ e f " y) I,o,.) Ix) I,o,.) IY) - Then PIX> 1] is ~f<itPIX>ll~ II) 38, I e (3) e For a r.v. X, if fx(x)~~(I<} ~ then P [; < X < a -.R; otherwise 0 1 1 (3) 3 (2) 2 "'<;fi.i>'" '" X 0< x<a J is ( I) 0 ~ ~, <it (I) 0 (4) I - 4 ~, -.R; fx(x)~~(I<} (347) ~ p[~<x<a] '!iT l!H 0 0< X<a """" Q1'1T I (2) - (3) 2 12 I 3 (4) I 4 l2P/22l/3l 39. If X and Y are two random variables and a and b are constants; then coy (X +a, Y + b) will be IX, Y) + ab II) ab coy IX, y) (2) COy (3) COy (X, Y) (4) None of the above II) ab coy IX, Y) (2) COy (X, Y) + ab (3) COy (X, Y) 40. Starting from the origin, unit steps are taken to the right with probability p and to the left with probability q(::: 1- p). Assuming independent movements, the expectation of the distance moved from the origin after n steps is ~ ~ q Ie 1 - p) iI; mOl 1 0 ~ fum ""'" '[<'! ~ ii 3m<'! ofT ~ ~ ofT """'" (I) 41. n{p-q) ..,a om; Of",""' i 1~ -..1 ...,n, om Of","" owff I '!Hit ~. n ~ iI; 'ITG 'l!' ~ ii "" M (2) (n-l)(p-q) (3) n (4) p-q n-l p-q If X is a uniformly distributed random variable in (-2a, 2a), then its probability density function win be ~ (-2" 2a) ij X -..T{ 1 0""," "~" '" (I) (3) (347) p iI; l!T'I 1 0 ~ <I'll 1 o 1 30 to iii ~ (2) -2a<x<2a -2a< x< 2a (4) 13 1 2a 1 4a '''",''01 .....,.. """" ~ -2a< x< 2a -2a< x< 2a (P.T.O.) 12P/221/31 42. If X - 'X. ~ I and Y - X ~2 are independent r. v. 's, then the distribution of the variate (X is (4) All of the above (3) X 2 with (n, + n2) d.f. (2) (3) X 2, (n, +n2) ""'"' 43. ~rr (n2' , n22) (4) ;m)u; '!itfl "" Let 6 f(x)=,,' x x = 0 and M(t) = '" x = l, 2, 3, ... elsewhere 6etx L~. Then which one of the following is correct? x=llt X (I) fix) is a p.rn.f. but M(t) is not a rn.g.f. (347) >!>fi (2) fix) is a p.rn.f. and M(t) is a rn.g.f. (3) fix) is not a p.rn.f. but M(t) is a m.g.f. (4) fix) is not a p.rn.f. and M(t) is not a rn.g.f. 14 + Y) 12P/221/31 6 f(x)~-,----,-' = ~ M(t) ~ ~ 6 Ix L:,", tl mM x",}1t ~ x n x o. L 2, 3, ... ~ i? if 1I -.iR-m "'" x (I) f(x) "'" 1110",0"'0 t ~ M(t) "'" (2) fix) "'" 111 0", "' t <I'll M(t) "'" ano"",o",o (3) fix) "'" 111 0", "' ~ i 'R'\! M(t) "'" (4) fix) "'" 1110",0"'0 ~ i ~ M(t) "'" ~ ano"",o",o i i ano"",o",o ano"",o",o i ~ i t 44 . 45. If Mx(t)~ [ l+e )" ,then variX) will be -2- .,ffi; Mx(t)~ll~e'r m(X) "" JImUl iPn (I) n (2) n 2 (3) The mode of the geometric distribution (I) (~r (3) (2) 0 I n (4) 3 for X I 2 = n 4 1, 2, 3, .. " is (4) Does not exist . (I)X "2 ,X ~ L 2, 3, ... "" "W"" iPn ~ 'R'! (I) (347) I (3) (2) 0 I 2 15 IP.T.O.) 12P/221/31 46. 47.. 48. Let X be.a standard normal variate. Then Pr (X >1 96) is l!Rl f.fi X 1!i'fi (I) a lfI'I'I; '~I",'" 'R ~I If random variable PIX>a+b/X>ajis. 1iI Pr IX > 1 96) ~ (2) 0'025 X (3) 0 05 has exponential distribution with parameter e, then (I) PIX>bj (2) PIX> aj (3) PIX >a+bj (4) I-PIX >aj The probability mass function for the negative binomial distribution with parameters r and p is (4) All of the above (4) (347) (4) 0'95 16 aWm ll'ft 12P/221/31 49. For an exponential distribution with probability density function ~ ~ tmri~ ~ ~ snfilCfldl ~ ~ f{xl",,!e-:<-/2; 2 X'2':O its mean and variance are (I) 50. (3) (~, !J (4) (2, 4) Let X have a Poisson distribution with parameter A. Then the value of F(O-5) is e- ic +Ae"}' 2 ( I) e i. (2) (3) e () 5;. (4) The value is not defined A. (3) (1) 51. (~,2) e -------- e-O SA The moment generating function of a random variable X is 4 3! 212t +---e 5 3 15 Mx(t)~--+-e Then E[X I is t m E[X l,rr.n (I) (347) 22 (2) 9 15 5 (3) 17 15 17 (4) 11 5 (P. T.O.) 12Pf221f31 52. 53. If X is a standard normal variate, then! X 2 <!Ii; X "'" lTR'fi 'ill" '''' "" (1) I, 2. 2 (2) t ill ~, PII (m, (3) 2. 1 2. 2' 2 q;] """ (4) 1, 1 (4) PI (m, n) -.Frr n) For the geometric distribution P[X = x 1= _1_. x 2x = 1, 2, "', the Chebyshev's inequality is (I) P(IX-21>2]<2 I 1 (2) PIIX-21>1]<2 (3) P II X-II> 2]< 2. (4) PIIX-11>1]<2. 2 3 If X is F(3, 4) and Y is F{4, 3), then for all k which one of the following is true? <!Ii; X "!fRl (3471 t ftm'liT """" -.Frr n (I) 55. 2. X 2 "'" 'IT'll. "" 2 If X - F(m, n), the variable m X is distributed as <!Ii; X - F (m, n), ill "" m X n 54. is a gamma variate with parameters 2 q;] """ F(3, 41 "'" Y q;] """ F(4,3) to ill k i\; <{>1\ trR't i\; fWl f.rq i\ i\ -.iR-m -.Frr? (11 PIX Sk]=p[YS~l (2) PIX Sk]>P[YS ~J (3) PIX ~kJ<P[YS ~l (4) PIXSk]+P[YS ~l=l 18 12P/221/31 56. The probability mass function of a random variable X i's given by pix) ~ {2}+1 o . . 2 . x~O'~ otherwise fl].IS Th en E 1- LX (I) (2) 0 (3) I I 2 (4) Does not exist P(X)~{2}'I' x~0.~2." 0, (I) 57. (3) I I 2 The number of possible samples of size n from a population of N units without replacement is (II 58. (2) 0 a:r;::<:/'lIT IV' In a (2) ~ample n' (3) (4) N! of 400 mangoes froma large" consignment, 40 are found to be rotten. The standard error of the percentage rotten mangoes is "-" """ ~ il) 55 i347) W!ur "it 400 awif it (2) ~ ij 40 >!TIl mT'! (3) 6 0 19 1 5 WI >W I mT'! awif <lit >!fum """" (4) '!ft 14'5 (P. T. 0.) 12P/221/31 59. A sample of 16 items from an infinite population having SD == 4, yielded total "scores as 160. The standard error of sampling distribution of mean is "'" ""'" m. ~ .f"~." (I) 60. """ "" 1!F!<O 1!F!<O ~ t. "'" (2) I 160 t<n t I llT"l if (4) 0-4 (3) 40 10 If the sample values are I, 3, 5, 7, 9, then the standard error of sample mean is (2) SE= ~ ~ ~ 1. 3. 5. 7. 9 ~ i. <it (2) llT'l!' = (3) SE=2 0 ~ llT"l "" 1!F!<O (4) I SE =- 2 ffi -.iPft I I 2 ,/2 Level of significance is the probability of (I) type I error (3) (2) type I and II errors m~ "". 62. ll<i\ "" ~ :f"'"f'!iI< 16 ffi -.iPft (I) SE=,/2 61. = 4 (4) None of the above "Ill,,"! t (I ) ~'I'l wm "" (3) ~'I'l "'" type II error ffi "" (2) ~ wm "" ffi'i\ "" (4) ~ wm "" l!R: "" ;m)m if 'il ~ 'f@ Let a and I~ denote the probabilities of committing type I and type II errors respectively. Which of the following values of Cl and p correspond to the decision rule "always reject the null hypothesis" ? (i) =0 (iii) ~=O (iii a. = 1 (iv) ~=I (4) {iii and (iv) Select the correct answer from the codes given below Codes: (I) (i) and (iii) (347) (2) (i) and (iv) (3) (iii and (iii) 20 12P/221/31 m-.i ..t.-"i\ (i) om: P ......' ilf; a a 'If.! ~ it"" "'" ~ JIiIiR <Ii) om: p ;\; f.t"l 'I1'i1 if "i\ "f.i"""n. qf'' ' ' ", 'iii ~ 31<41"" it" ;\; ~ "iii\? f.!uf>I-Wm (ii) a 0 (I) (i) "'" (iii) 63. w:m <Ii) .,fli,,",~ ~, a (2) ~ I (i) "'" (iv) (iii) P~ 0 (iv) P~I (3) (ii) "'" (iii) (4) (ii) "'" (iv) Match the following correctly: Hypothesis A. J..L:= J.i.o. B. 0 2 :::: C. D. Test distribution I. t II. F p~O III. Normal Pl.23 =0 IV. X (}"2 =2 10 (I) (A, II) (B, Ill) (3) (A, IV) (B, I) f.t"l 'iii '!!tl JIiIiR (C, IV) (C, 11) 2 (D, I) (2) (A, 11I) (D, III) (4) (A, I) (D, I) (2) (A, 11I) (D, 11I) (4) (A, I) (B, IV) (B, II) (C, I) (C, III) (D, II) (D, IV) 1Ptfuo ~ : it q fJ. Cf) (rlI "II (347) A. ~l=)lO' 0 B. 0 C. p~O D. P l.23 2 2 =2 0=10 I. t II. F 11I. IV. =0 (I) (A, 11) (B, III) (3) (A, IV) (B, I) (C, IV) (C, II) 21 (B, IV) (B, 11) (C, I) (C, Ill) (D, II) (D, IV) (P.T.O.) 12P /221 (31 64. Let'(X\X 2 ) be a random sample from a gamma distribution 0(1,8). Then for testing HG: (~ = 1 against HI : 8 'lH1 Ii!; WI! m GILS) 'Vt~'!UJ 1; fu1( "ifuq; = 2, a critical region <l (X I X 2 )"'" "'0'''''' ~~) H,: 802", ~ Ho:Sol", i\tr is obtained such that P[CjHoJ=O OS. Then the power of the test is II) 65. (2) 0-95 To test Ho: ~t = 0-05 (3) 0-85 (4) 0-90 f.!o vs. HI: IJ. > J.lo from N (~a2) when the population SD is known, the appropriate test is (I) (-test N (f, a 2) (2) it ~ ~ H,: ~ > ~o "' ~ H 0 : fL L~t (4) None of the above 0 fLO "' WIW'T "' (2) Z -W\'!UJ T be a statistic based on a random sample of size n from the population f(x, 0) and E{T}-=:O. Then }v-a VITI is distributed as (1) normal for large n (3) (347) fu1( ~ WIW'T ~ <Illfu """" to]i'MT (I) t-WIW'T 66. Z -test (2) sameasf(x,S) normal irrespective of size n (4) None of the above 22 12P/221/31 _ fi!; T ""8 ~- wrll! CfiT fix, 8) i1 .,,R"" ~ 'R n """"' ~ 3l1"I1fur .R,,~,i~ T t 3i'r< EIT) =01 <it . 'ijf~ ~V(T) (I) ~ n ~ (3) 67. f(x,8) fuir '~I"I'" t\ tim In los sing of a coin, let the probability of turning up a head be p. The hypothesis is H 0: P = 0 4 vs. H 1 : P = 0 6. H 0 is rejected if there are 5 or more heads in six tosses. Then the size of type I error is _ fi!; l('!i m ~ ~ 'R, HI: p =0 6 tl Ho """' <lit (I) 68. ",,,,1,,,, om 3lf.\ <lit "fl1"dl P ~I q~",,"", Ho: P =0 4 ~ tim '1ft: 5 <IT an"," 1m ,,: "" ~ 'R lI11! ,;\it ~I <it """ 1m ~ Wi: '"' """"' tim 0'041 (2) 0"037 (3) 0"029 (4) 0"05 :2, "', X n is a random sample of size n from Poisson distribution with mean A, the Cramer-Rao lower bound ~o the variance of any unbiased estimator of A is If Xl' X <W: X:, X" P', X" 3WlT'l n '"' "'IRil oir-! i1 "'" 01"""" ~ ., ~ '"'" A ~ <lit tm-U'l "l:l <fi'lT tM\ f->e~ *"__ """" [I) e" (2) A (3) A random sample Xl,X2, ,Xn 18 t <it A~ -< 5 (4) n n '" 69. tim e n observed from N ().1, ( 2 ), where 0- 2 is known. Consider the following quantities n It X2 n I-t lit i =1 CJ I (X, -fL)2 ioel Which of the above are Statistics? (347) (1) I and II only (2) I, 11 and IiI only (3) III and IV (4) 1, 11, III and IV 23 IET,G.) 12P/221/31 N (I'. ,,2) >I, ~ t ,,2 >m! -.;0; .,<;R0.. '!Ifu<.>f XI' X 2' "., X n ~ ~ '5!l1l1 iI '1f\lnui! '" Wm ~ : n 1. LX? H. i _,I 3'li\ifi 70. ~ >I ",",-llT t X~2 j,=1 a III. .Iii~.f", ~? (1) ~ I 3it( II 12) ~ I, II 3it( III 13) III 3it( IV (4) I, H, III 3it( IV A sufficient condition for Tn to be consistent for (1) E(Tnj----)B as n-t (2) V(TIl)~70 (3) E (Tn) OCJ as n"co - 0 or V (Til) -t a as n -)0 00 (4) l>(Tn) --> 8 and V (Tn) --> 0 as n --> (I) E(Tn )--> 8 "'" n--> (3) E(Tn) --> (347) tlX, _~)2 j-"J a """" 00 00 V (Tn) --> 0 "'" n --> 00 24 f) is IV. &. (X;,,-~ r..",r",ru.o r 12P/221/31 71. For a frequency distribution, a two-parameter normal distribution was fitted. The observed and expected frequencies in the various classes are given below : 'I""''''' m ~ ~, 1('n " ~ -.r.l "~'"'''' ltf"" 3it< """~'d "d'~ -;fti\ <l\ ~ t : 1('n "'..... m qi\ ~ ~ Class q>f 1 2 3 4 5 6 Observed frequency 6 14 20 19 16 6 4 15 21 21 15 4 'l'lT1 ~ -.>if if ftf~ ilH1=4lRdl Expected frequency Jl~I~la ilHJ:ilHfll Then to test the goodness of fit using the 'X '2 -statistic, what is/are the degree(s) of freedom of the X 2 -statistic? X 2 "fd"r~ "" m ~ ~ ~ "" '!tl~ -.i.i ~ ~ X'-"fdQ!f~ <iii ~ -.ilfl (m) "'" tit 7 (I) 72. 5 (2) 3 (3) 9 4 Let t be a Student's t-variate. Which one of the following is identically same as F ( 1. n) ? (1) t 2 with one degree of freedom (2) X2 with one degree of freedom (3) t 2 with n degree of freedom (4) X'2 with n degree of freedom (2) 1('n ~ (4) (347) (4) 25 -.ilfl ..-r<'!T X 2 n ~ -.ilfl ..-r<'!T X 2 (P.T.a.) 12P/221/31 73. What is the maximum likelihood estimator of p based on a single observation X from Bernoulli distribution with parameter P 1ITifeI P E [ ~. ~] "Iffi ~ mit""", It..,ur (2) Let [~, ~ J? X 'R :mmIt! p "" ~ W'ITflrn ~ ~7 ","-w 74. E XI, X2, "', 2X +1 (3) 3X +1 7 (4) 7 xn be a random sample from f{x, e J = e-( X-B); X 7 x> e, 0< e < co and zero otherwise. Then a sufficient statistic for 9 is (1) Max (xl,X2,"',XI'lJ (3) LX, (4) 'tl"RT fcfi, !(x,8)=e-(x-e); x>9, 0<9<00 (f~ ~ 3FllWT, ~ xl,x2, .. ,xn 1l.'=fi 411RbCfl ~ ~ I '" 8 "" 'l'lflI .[li<;,[", (3) 75. IT Xi tit'lT LXi (4) IT Xi If X 1,X 2 ,"',X n is a random sample from a population then the maximum likelihood for 8 is (I) ~xi n (347) EX 2 (2) - - ' n (3) 26 )EX? n (4) ~~X?/n 12P/22l/3l 76. If X is a sample mean from the binoIhial distribution b(1, p), then (1) x is a sufficient statistics for p (2) x is an efficient statistics for p (3) both (I) and (2) (4) None of (1) and (2) (3) 77. (1) 31'R (2) <:Hi (2) X, P 'fi1 1% ~ (4) (1) 31'R (2) if il .Rl"\,,, ~ ~ 'f;il If the density function of a variable x is f(x,9)=ge- ox for O<x<if.J then 95% central confidence limits of 9 for large sample n are (I) ( 1 96',_ l -rn r (I) (I+~) - In x(3) (347) ('! ~~,;?~) x (4) None of the above (2) (1 ?n6)/x (4) ~ffi; 27 if il ~ 'f;il (P. T. D.) 12P/221/31. 78. Xl. X 2. "', X n. represent random obseryations from the distribution Which one of the following classes of estimators correctly character the family of MVB estimators? (I) X (2) AX +B. where A and B are constant (3) f(XI. where f is a uni-valued' function of X (4) all polynomials in X, where X = (~Xi) n ..m ~ '1~R0 .. jt~ q;) f.'R<;f1ffi ~I f,1 ... Mru.d "'I.. " .. q>jj i! ~ ;fi\;f-m .". "I:"f'! """" (MVB) 3l1 .. " .. " "" ~I\I"H <n !T i? (I) X (3) (347) fIX), 'Il'i f, X "" .". ~ '""" i 28 'Iftoi'l 12P/221/31 79. Let (X 1X 2 ) be a random sample from N{8,I). Then for testing H o :8=9 0 against HI: e >8 0 lIT'! ~ ill; which of the following is UMP critical region? NI8,1) " 'll\l\I"I ~ ~ M 80, (X I X 2 ) -.;ifuq; ~ "'~" ~ tl HI:8>8 0 ~ il<><: Ho:8=8o~ """ i\ """ -"lIT ~ UMP oTm? Let 'lFITilI; X1 X =Jl+El 2 = 2j.J. +E:2 Eland E2 are independent with same variance a 2 Then BLUE of Jl is (2) Xl +2X 2 5 81. If X is a binomial variate with parameters (5, 8), the UMVUE for '1'(8) =8 (1-8) is -.m; M ~ '" ~ (UMVUE) X fuliI; "!!T"ffi (5,8) t i\ '1'(8) =8 (1-8) 'lIT W!T'rn: ~ lIWl 3FIh oTm (2) (X2 -5X)/20 (3) (347) X (I-X)/20 (4) 29 XIX -1)/20 (P.T.D.) 12P/221/31 82. If Xl, X2. "', Xn then are the values of random sample from a normal population N (Il, 0'2), =_1_2: (x, _x)2 S2 n -I is a/an (1) unbiased estimator of t'f2 (2) sufficient statistics for 0'2 (3) mean squared error consistent estimator of All of the above (4) 'lfi; S 2 1 n -I (3) 2 N(~,a') "" 'lTV! q<f lIt~'*' <l ~ 'lH t ill (lft Wm ~ ~ 51fu;;~f-&1 (2) 0'2 (4) mTm <Nt q:jf Let a population of size N = 10 have mean 15 and variance 100. A SRSWOR of size 4 is drawn. If Xn denotes sample mean, then E[ X~ 1is Jli;lfi 311il'iR N ~ 10 <1;1 Wlfu "" fu>n 'l'l1 (I) 140 il 'lfi; ~ 'IT''' (2) Xn t 'lTV! 15 <I'!T JmtUT 100 ~I 311il'iR 4 "" 1('!i SRSWOR ill E(X; J ~ (3) 225 240 (4) 150 Which sampling design is most appropriate for cluster sampling? (1) Simple random sampling without replacement (2) Simple random sampling with replacement (3) Stratified random sampling (4) Quota sampling (347) ~ ~ "" 'Rf'R<f ~ a' lJHI Jli; 84. - ~--L(Xi-X) Wlfu SI<!;'II"'I 1""'"1 Xl, X2, "', Xn. (I) a' 83. 0' 2 30 12P/221f31 .Iii,,"" ~ ~ >rll! ~ t? ~ <I%<! "'~Rl>...Iii,,"" '""'''"'''. "'~" .Iii,,"" "f<!ftr "'~" .Iii,,"" .ro .Iii,,"" ,,;r., --.1\ .Iii~., '1hr.rr ~ ~ (I) (2) (3) (4) 85. m<1 m<1 Supposing that, in cluster sampling S~ represent the variance within the clusters and st between clusters. (1 ) wn ~I ~ ~ S,; ail, .Iii,,"" it, S~ ~ ~ ~ S~ ~ oifq <l"P'T '<'IT (2) S;' ~ 86. (3) S~ ~ S~ (2) S~ ~SE 2 = S2 S6) b 'lHT fiI;, What is the relation between S~ and S~ ? >1m"! 'iii afu: S~ (4) None of the above ',Jy;ffi ~ oifq >1m"! 'iii ~ i? SE (3) S;,:o; SE Consider the following statements : Assertion (A) Non-sampling errors are present in both census and simple surveys. Reason (R): Non-sampling errors are caused by factors beyond human control. Which one of the following is correct? (11 Both (AI and (R) are true and (R) is the correct reason for (A) (347) (21 Both (AI and (R) are true but (R) is not the correct reason for (A) (31 (A) is true but (R) is false (4) [AJ is false but (R) is true 31 (P. T. 0.) l2P/22l/3l f.\",lflfuiH ~ 'l1: ~ ~ : '""" (A): ","1'<1",., ~ ~ ~.'IOHI """" {R) : ","1'<1",.. ~-m W"! f.\",r"fuiH i\ 1I 87. ~ 3'! ~ 1I ~ ""~ (I'll .r.tl ~ t '. a1t< (R) <ir.i\ W"! ~ (2) (A) a1t< (R) <ir.i\ W"! ~ ~ (R). (A) '"' ~ """" '!g'f (3) (A) W"! (4) (A) 3lW"! a1t< ~ (R) 3lW"! t .r.tl~1 .n llFI'ftq f.t>i-.ur 1I <R .r.tl ~ 1 {l I {AI t <ir.i\ i\ f1ro<tF! ~ {RI W"! (RI, (A) '"' ~ """" t t t t A population of N units is divided into k strata whose sizes are N I N 2. N k-l and N k respectively. If the number of units selected from the jth stratum is "'J n f (j = 1, 2, .... k) in case of proportional allocation, the sample size is n N (l) n = - n (2) _ J =_ Nj N nj (4) None of the above N ~ ;;IiI 1('0 W@ q;) k ~1 ~ ~ "":1"1'<1 .. f.'!> R '"' 3lJl!1'! "m i\ .m ;;IiI ~ 'T<l ~ 3!T'IiR lI"m' N 1 N 2 ... , N k-l i\ jl w: ii 'fIIf.ffi ~ ;;IiI t N (I) n = - n" n (2) _ J =_ NJ nj (347) t 32 N m..r a1t< n f (j = ~ 2, .... k) m. Nk <IT 12P/221/31 88. In SRSWOR, probability of a particular set of n units selected as the sample, is (where N is the population size) SRSWOR ij n -3!Jl11'ft ~ will! "" (I) 89. 3W!T'l mr. ~ ~ ~ ~ <"! ij ~ -;if.\ <iii ,,10,,", -;;PIt (~ Nt) ~ n (2) N (3) N I N" (4) Match the items in List-I and List-II correctly List-ll (Variance) List-J (Statistic) 0 2 0- 2 A. Xl -X2 P. - ' +-'2n, 2n, B. Sj -S2 Q. (I-e')' In c. r R. . S. _1 0"2 +--1. n, n, D. Median ,,' 2 n 0 2 Code,' (347) A B C D ( I) S P Q R (2) P Q R S (3) Q R S P (4) R S P Q 33 (P.T.O.) 12P/221/31 'i'fi-I 'i'fi-II t lI'IT l!<;\ q;) ~ ~ <[!it-I <[!it-II Mil",,,,) (J1mlIT) P. 2 0'2 0 +_2_ 2nl 2n, _I Q. (I-e')'/n c. R. r S. n ,,' 2 n 2 0 _1 nl (I) ABC D S R P Q 2 0+2 n, (2)PQRS (3)QRSP (4) 90. R S Q Let p be the intra-class correlation coefficient between elements of a cluster in N clusters of M elements each. The cluster sampling is more efficient than the corresponding simple random sampling without replacement if '!R1 ~I ~ M """"" qffi ~ N ~ it mft ~ t """"" t oil<! ~ "$"""~ ~ "" ~ "" """". I (I) p > - - NM (347) P ~'lf.fi ~ t\t<l (2) p "!ffi'! ~ _-:-;:-1;--:- .,f<>.. """". (3) p< NM-I 34 N~-I it 3lflr.!; <;!!I ti't>rr. ~ (4) P > _ --;-::,1;--;NM-I p 12P/221/31 91. If population size N := 100, sample size n = 12, then the ratio of variances of sample mean in SRSWR and SRSWOR is 'If!; m ~ N ~100, ~ ~ n ~12 '"""""'" (I) 92. <m'I "'<;Rio'" 135 8 "fu", .. (2) ij ~ m, ""." "4 (3) (4) ",~fi;0," "fu ... ". <1m 'l 8 In stratified random sampling. with the cost function C =C o +ECnn n the variance of ~ il1iiNsl!:fl SlRtilil."'l ~ imT, .q, is proportional to nn ~ <'Xi<l ~ C =C o +I:Cnn n ~ nn ~'1'jq,"l m, 'iqY~P"lIf.1d lff\."lJ Y st q)! m:RUT. imT The condition in which double sampling method is more precise than taking a simple random sample for the same cost, is obtained as . " ftrnif ~, "Ill", .. 17& d'"" ~ &<rr to ~ "'" ij (I) 94. 25 22 the estimated mean Yst is minimum, when 93. <it "fu""q. U%<l <m'I iii -.mui'f "'hi ~ imT If P 2 > 4cc' -=--,.- (l<r x and X 1('h >m! 1!l ""'" iii &<rr %? 4cc' <'IT'! fuu; '111, 1('h <m'I 4cc' (3) p2>_=~ (C+c')1/2 (2) p2 > --'=~ .(C+C,)2 ",~fi;0," ~ "Oil "q'iIT (4) p2 ~ 4cc' denote the sample and population mean respectively and R is the ratio of , popUlation totals, then in simple random sampling, bias of the ratio estimator R is given by 'If!; x 3ii1: X lI"m' ~ afi, , (I) COy (R, x) x (347) m 1lM t 3ii1: R m , (2) COy $if , (R, X) (3) x 35 COy (R, x) X "'hi ~ t m <m'I "'<;Rio'" , - (4) _ cov(R, X) x (P.T.O.) 12P/221/31 95. For a 2 n -factorial experiment in r replicates, the. sum of square for the effect A in the ANOVA table is (I) 96. [A[2 8r (2) [A]' 2r (3) [A]2 [A]2 (4) 16r 4r In a randomised block design with 5 blocks 6 plots each if MSB SS = "140, ~hen MSE is = 10, MST """ "<;Ri><fiI'fd ""'" ~ if, fomij 5 ""'", 6 ~ qffi ~ ""'" ,",'1'-.'\' '"''1'-.'\' = 15, 'r'f q>f <im = 140 to <i\ '", ~ <im -.Pn (I) 5 75 97. (3) (2) 57 5 (4) 15, Total = 10, 3'l"!R 12'5 With the usual symbols, the estimate of a missing value in a RBD is tB+rT-G (1) - - - - - (r-1I1t-1) (3) 98. 1 25 = (2) rB+tT-2G (4) (r -lilt -1) rB +tT-G (r-1I1t-1) rB+rT-tG (r -lilt -1) In an analysis of variance problem for one-way classification with three classes and three observations in each class, the F-ratio is 1 5 and the total sum of square is 18. The mean square between class will be 'fi\1I1"i\ i<; UT'! <It.! "'" i<; 'll.'"'! .,Il<t;{O, i<; fait """" ~ om W"f q>f <im 18 ~ I "'" i<; 'It." i<; ""." q>f "" l!R -.Pn """" q>f if <It.! "" 1-5 (I) (347) 2 (3) 3 (2) 8 36 "",;,,0, WR<!T if F-~ (4) 6 12P/221/31 99. In a 2 3 -factorial experiment, the treatment effect 11.'" 2 3 ";;0",,41 3lfmeiM i\ 0'RlR ~ ""'" .!:. [(abc) + (ab) + (c) + (1) ~ (be) ~ (b) ~ (ac) ~ (a) J n is due to (1) 100. Let A, B, C, D be four treatments, then which one of the following can be considered as layout of LSD? _ flI; A. B. C. D ;m q;wo 'A ( I) t Ic ! B D C D A B jE C D I iD c A B rA C B D A C (3) D B A lA D B (2) A C D B (4) C A ~ q>f ~ "" ",,31m _ "l1 A B B A C C C D D D A B D B A C D B C B C A D B C C D A B C A D Ifthe'degree of freedqrn for error SS in a LSD is 30, then the order ofthe design is ~ mit ~ q>f ~ i\ ~ (I) 4x 4 (347) <it f.!R if it ..:t. 11.'" ~7 '""'" 101. (4) A (3) BC (2) AC AB ': q>f m t! """'" (2) 5x 5 (3) 6 x 6 37 W 30 t, <it "'" ~ "" 3lT<!iR (4) 7x7 (P.T.O.) 12P/221/31 102. Match List-I with List-II and select the correct answer using the code given below the lists : List-II List-I A. Replication is used {al For validity of estimate of error B. Randomisation is used (b) For diminution of error C, Randomisation and replication are used (el To achieve the independence of error D. Replication and local control are used Code: ABC D (I) (d) (e) (b) (a) (e) (d) (a) (b) (3) (d) (e) (a) (b) (4) (e) (d) (b) (a) (2) 'f'll-I q;) (d) To estimate the experimental error ~ ~ 'f'll-u <I ,,;n 'f'll 'iii ~-I A. B. C. D. ""' r " m "'<;R><lil'0(01"5T'<1'T if , if .nn ~ (a) ~ 'iii ~ 31"Tffi ~ (b) ~ (e) ~ <lil ""'r" m ""'r" ,,;n.niH.~ ~ m if 'Ii" A B C D ( I) (d) (e) (b) (a) (e) (d) (a) (b) (3) (d) (e) (a) (b) (4) (e) (d) (b) (a) (2) (347) WI 'l1l. 'F 'fiT m ~-II 31"Tffi .1~Rl><fI''''"',,;n if ~ 38 'iii "OCR <lil ~' !T 'iii fu1( 'iii fu1( "'""dl JI11! ~ 'iii fu1( -.;< ~ 00< ~ : l2P/221/3l 103. For flxed effect model Yij=J.1+ti+~j+ey, i=l,2, .u; j=l,2, .b what is the linear unbiased estimate of - .. -Y.n ( I) Y 104. (2) iiI. -ii.. t 1 -t"4 - .. (4) Yl.-Y (3) Y .. The probability of rejecting a lot having p as the process average defectives is known as '(1) (2) consumer's risk "-" BTl f.m<Iil (I) type II error (4) All of the above (3) producer's risk >IlIil! l!1<>1 Wl P ~, -.i\ 31\41 .. " -.;f.\ <fil oq>iImT "" ~ ",ill..d' ;;n;f\ omit t (2) ~!IlI;R (4) 105. ? <fil Wl ;;Wu; <M\ In Wald's SPRT, for Ho: P = Po against HI : P = PI{> Pol regarding bip.omial proportion, consider the following values of the OC-function L {pI : ",ill.. """" i\; 3!~""''' d, 3f:l'!1d 'Iil~ SPRT i\; ~ it ~. a",~q'd i\; ~ it Ho: P ~ Po "" HI: P ~ P I (> Po) iI; ~ 'Iil~ -.;f.\ iI; ~ ~ ~ (OC) """' L (p) iI; R",Rlf@d l!f.i\ (i) 'It flr<m L(po) ~ : (ii) L(pd What is the correct order of the values of DC-function? ~ ~~ (347) (OC) """' iI; l!f.i\ "" ~ "'" "'" ~? (I) (i) < (ii) < (iii) (2) (i) < (iii) < (ii) (3) (ii) < (iii) < (i). (4) (ii) < (i) < (iii) 39 (P,T.O.) 12P/221/31 106. The graph of the proportion of defectives in the lot against average sample number is ~C-curve (1) 107. (2) ASN curve (3) Power curve (4) All of the above (2) (3) (4) ~ ASN 'Iji; 'Iji; <Nt In sequential probability ratio test, the lot is rejected, if (with usual notations) the following inequality holds 31j'" Ill" ., Ill,,", 31j'ffiI <rt\&l"T if me ~ M ~ (""'"" ~ if) f.tq 31" q "" , "" 'l1B'! oPn (3) Am ~-~- 108. Type 'A and type B ~C-curves >-~ 1-a (4) A m ~ 1-" differ from one another in respect of (1) hypergeometric and binomial probabilities (2) finite and infmite sizes of the lots (3) consumer's and producer's risks (4) All of the above A am B lI'!iT( iii OC-'Iji; 1l.'"-~ " ~ am ~ .,Ill,,", 3'l>iTffiT am 3,"'G'l,,~f "" ~ (I) ~uitw (3) 109. (4) ~ am 3W1l am;R iii me <Nt An additive model of time series with the components T, S, C and I is (I) Y~T+S+Cxl (2) Y~T+SxCxl ~T+S+C+I (4) Y~T+SxC+I (3) Y (347) <Rq if i>rn ~ (2) <fifi'Iit 40 12P/221/31 110. The equation of the parabolic trend is y ~46 6+2 4X -1 3X 2 If the origin is shifted backward by three years, the equation of the parabolic trend will be (I) Y ~27 7-5 4X -1 3X 2 (2) Y ~51 1-5 4X -1 3X 2 Y ~51 1-5-4X +1 3X 2 (4) Y ~51 1+5 4X +1 3X 2 (3) 111. The lowest ASN curve of a sampling plan as compared to any other sampling plan under similar conditions is considered (I) better (2) "'" ,RiO,'" ~ "" inferior (3) useless f.rqoq ASN "'" <Plf.! ~ if M (4) None of the above OR 511<1",." ~ <lj\ ll""" if llR1 ""'" t (1) 112. ~ 3-sigma control limits for the proportion of defective p', are , 1 )p'q' , -,CL~p 3 n (2) VCL~p+- (3) VCL~P'+3)P~q'. Cj.,~p' (4) VCL (347) (3) ~ ~3p' +)p~q'. CL , 1 )p'q' 3 n andLCL~p--- and LCL~P'-3)P~q' ~3p' and LCL ~3p' -Jp~q' 41 (P.T.O.) 12P/221/31 ~ p' i\; ~"':lq'd i\; fero. 3-funn (1) UeL~p,+)3~q', eL~p' <I'll LeL~p'-l~q' (2) UeL~p'+!:-JP'q', eL~p' <I'IlLeL~p,-!:~p'q' n 3 (3) ueL (4) 113. ~ ~ ~ 3 ~ p' +3~ p~q' , eL ~ p' <I'll LCL ~ p' -3~P~q' UeL~3P'+~P~q', eL~3P'<I'IlLeL~3P'-~P~q' In ratio to trend method, the median of the rend free indices for each free period represents (I) the seasonal indices (2) (3) irregular variation 31"j'lTd (1) (4) regular variation <i\~<ft" ~ auq<f i\; fero. ~ <mf\ ~ (2) ~ ~'Iit 'lit 'lit (4) f.i'lflffi ~ 'lit For the given five values 15, 24, 18, 33, 42, the three years moving averages are ~ (347) cyclic variation i\ JIijfu :5I"ffi'ft if, JIijfu ~ ~ <lit 111M,"' ""'"' ~ (3) 31~"flId ~ 114. n >W 5 lIT-if 15, 24, 18, 33, 42 i\; fuiI <IF! -.:Ml'! ~ l!T"'l (1) 19, 22, 33 (2) 19, 25, 31 (3) 19, 30, 31 (4) 19, 22, 31 42 m>n 12P/221/31 115. In case of multiplicative model, the sum of seasonal- indices is (1) 100 times the number of seasons (2) zero (3) 100 (4) 400 2''''*'' 1lflw-! <!i\ G>T1 ii, .;16"1. ~ 'liT -.iPT ~ (2) (3) 116. 'PI (4) 400 100 If the index number of 1990 to the base 1980 is 250, the index number for 1980 to the base 1990 is ~ 1980 311"" '1<, 1990 <!i\ ~ <i&rr 250 t <iT 1980 <!i\ ~ <i&rr 1990 311"" '1< -&m (1) 117. 4 (2) 40 (3) (4) 440 400 The values of gross national product (GNP) and net national product (NNP) follow the relation (I) GNP=NNP 118. (2) GNP<NNP (3) GNP>NNP > NNP Purchasing power of money is estimated by the formula (2) (1) Price index x 100 (3) (347) (4) GNP 100 (4) Price index 43 Money income x 100 Consumer price index Price index 100 IP.T.O.} 12P/221/31 "" <lit ~ (1IC'!) ~ (I) '!!"l (3) iftiij- ~ 'liT ~ -- ~ <m "['l'fi x 100 100 mn tl "" """ (2) iiliih!ii '!!"l (4) '!!"l "['l'fi x 100 "['l'fi 100 119. The condition for the price indices to satisfy the circular test for four years data is 120. If the group indices are 80, 120 and 125 and their respective group weights are 60, 20 and 20, the consumer price index is ~ "'!!' "['l'fi 80, 120 3i't( 125 ~ 3i't( ~ "'"' "'!!' 'lR 60, 20 3i't( 20 t <it "3'l'1lmr '!!"l 'L"'" ~ (I) 121. 108 33 (2) 97 00 (4) (3) 98A9 49 98 If Laspeyre's price index is 324 and Paasche's price index 144, then Fisher's ideal index is (I) 234 122. (2) 180 (3) 216 If PI and P2 are the population at an interval of 10 years, the population just after five years 'Will be (3) -1 [1 -+1 2 PI p2 (347) (4) 200 44 J 12P(221(31 123. If P j and P2 are the population at two census conducted at an interval of five years, then formula for "the growth rate of population is 'l1l; 'lfu "'" if; ~ 'R ~ ~ ~ ~""H,ai\ il J!lll ~,<i","1 P, 1('i P, m. <it "ffii"", olil ijf.l; <:< "" 'li' i (3) iF; r ~s!'1 _1 \ P, 124. The probability of living of a person in the age group x to (x + n) can be obtained by the formula (1) iX_+_r!_ (3) (Ix -IHol Ix 125. (4) lx+ TL lx+n If Ix is the number of persons living at the age x anq. Lx the number of persons living in the mid of x and (x+l) years, then the relation between Ix and Lx is 1 (1) Lx =-Ux+lx+d (2) L (31 Lx (4) 2 =: 1 , I x x ~-+I 2 x None of the ahdve H- 'l1l; OR x 'R <llfiffi ~ olil <i"&rr Ix i afr< x afr< (x + 1) 'l'l if; "'" <llfiffi ~ olil <i"&rr Lx to <it Ix afr< L x if; oft"! ~ Wn 1 ( 1) Lx ="2 (lx +l.HIl (3) ::= Lx l , I H- (3471 45 x 2 (2) Lx (4) ~ ij ~-+I x -a ~ 'Itl (P.T.O.) 12P/221/31 126. The death rate of babies under one month is -!mown as (1) neonatal mortality rate '(2) infant mortality rate (3) maternal mortality rate (4) foetal death rate .."" <lit "'" ~ ~ (1) ~ 'Rl 127. (2) ''IT'f\ -.mit ~ 1 (3) ~ 'Rl For M / M /1/ N queue model, the probability Po. that there are no customer in the system is { (1) Pn "" l~e l-e N + 1 e~l 1en (2) (3) p n ~r+eN", ' e~l (4) Pn = reN,' 1 e=I , e~l N +1 , e=l If arrival rate is 3 customers/day and service rate is 5 customer/day for M / M /1 queueing system, the expected number of customer in the system at certain day is (1) 1-5 (2) 5 1m'!> ~ t <iT (4) 2-5 (3) 3 2 .ro Let Ls be the expected number of customer in system and c expected number of busy servers providing services and Lq the number of customer in a queue. When Lq = 0, then 'lR1 fif; <i'! if "'" II> '" JlWIij <lit 3fu: -..m: if JlWIij <lit m..rr L q m..rr L, 3fu: c "i'li ~ '" ""'" ~ I "'" L q ~ 0, <iT (2) L, >c (347) e=l e 'Ifi; M / M /1 -..m: <i'I if JlWIij ~ aif.t <lit 3 1m'!> ~ 3fu: <i'! if M f.ifffir f<;.! """~Id JlWIij <lit <i"&lT -.?t>ft 129. e~l 1 e N +1 - - en r~e Pn;;o; e N + 1 e=:l N +1 128. f<m "'" if ftrlJ 'Rl 'Rl >fur( (3) L, 46 ~C .ro """ q;f.t (4) L om:\ ~ <lit c , ~ 2 m..rr 12P/221/31 130. The passenger and the trrun in queueing system are (1) customer and server (2) server and customer (3) both server (4) both customer 'IT'fi 3itt ~ 'f;<m <i-. i\ ~ (2) ~"~'d' (I) 1m'" 3itt ~"~'d' (3) 131. -.;HI ~"~'d' >itt 1m'" -.;HI 1m'" (4) In some simplex table of minimization Lp.p., the column corresponding to a variable x j is {2, -1,0, _3)T. The Zj -Cj is most positive. Then (1) the solution is unbounded (2) the solution is bounded (3) the solution may be bounded or unbounded (4) None of the above "L""""% l.p.p. 'Itff 3lfue; _ (I) '"' ~, '<I< Xj '" (2) '"' 'ii!<: ~ WI<! ~ (2,-LO,-3!" ~I ZrCj cit ~i (3) '"' 'ii!<: '!T 132. <fit fi\;<ft ~'<d'" ~ i\ '&'n (4) i ~ i\ i\ ~ 'Itff The optimal basis of primal consists of variable Xl and x 2 , The costs of these are 3 and o and the corresponding columns are (3, 2)T and (0, -lIT , Then the optimal solution (YI' Y2) of dual is 3!T!l (~) '" ~ 3l1>m i\ 'ill XI 3itt 3itt (0, -I)' tl cit ~ "" ~ '"' (1) (3,0) (347) x2 il ~ (YI' Y 2 ) 47 3 >itt 0 <f'!T WI<! m<'Il (3,2)T '&'n (3) (1,2) (2) (L 0) <Ii\lm (4) (0,0) (P. T.O.) 12P/221/31 133. Given Min -3xl -2X2 subject to Yl XI-X2?>:1, -3x\ +2x2 2': -2, Y2 Xl 2': 0, unrestricted in sign X2 The optimal solution is (I) XI 010, x, 0-11 Xl - x2 '2': 1, (2) XI 01, x202 (4) Xlox20-1 Yl -3xl +2x2 ;::;: -2, Y2 XI '0, x2 134. (347) Fro "it ""'" The component useful for long-term forecasting is (I) trend (2) seasonal (3) cyclical (I) ~ (2) q'iolft. (3) 48 ..tl<T (4) irregular (4) >lR.fiI, 12P/221/31 135. The component useful for short-'term 'forecasting is (I) cyclical (3) seasonal (2) trend (I) ~ 136. (2) JI<!ftr (4) irregular (4) ",f.I"liId The missing value for the following data x 5 10 IS 20 y 2 5 ? 8 by me binomial expansion method' is '" ~ ~ JmRUl AA1:IU. (I) 7 137. WI 1!H -.T>n. (3) 3 (2) -7 (4) 25/3 If Y~f(x) and the values of fix) for given x are f(I)~14.J12)~I2,f(5)~6 and then f(7) is n81~21, am ~ Y~f(x) flT( x i\; fu1( fix) i\; ~ fll)~14.J(2)~12.J15)~6 (2) (3) -8 12 f(8)~21, <it (4) 10 If AYz is constant, then Y x maY:be (I) constant (3) (2) at equal intervals Both (I) and (2) ~ ~yz 3'ffi to <it Yx (4) None of the above -.T>n (1) _ (31 (11 (347) am -.T>n (I) 2 138. irH (2) WIR am (21 *il "''''''<'1<k (4) =l;n 49 11 *.~ '!lff (P.'1'.b.) 12P/221/31 139. The relationship between u of Stirling's formula and v in Bessel's formula for interpolation is I.q-O. I (3) u=v-- (2) u=v-l (I) u=v+1 2 I (4) u=v+- 2 If the temperature of three dates of June, 1994 were as follows ~ ~, 1994 <lit -.ft:! 1i1tl1!il "ifi\ Dates "ffi'I'IF! "f'J 1 10 25 33 38 46 ~ lI'IiR 'IT , 1fTfmI Temp (0C) ffi'i>1R (0C) The estimated temperature for 20th June, 1994 by divided difference method is <II mrr 3MR ~ ~ 20~, 1994 (I) 43 37 141. q;j ""'""" (2) 42 37 "ffi'I'IF! ~ (3) 43 73 14) 39 0 Relation between V, .6. and E is (2) E V A (4) None of the above (3) VE=EV=A V, ~ VEE -~-~ om E ~ iIT<I ll'4l"l t VEE E V A (2) - = - = [4) ~ 142. If f{xl = ~ fIx) (I) n (347) if "il -.;'tl ~ xTt. then [(x,. xr+tl is a homogeneous expression "in x r. xr+l of degree =x", <II f(x" X,.,). x" x,., if 'Iitf?; q;j 11;'n ",,","'" ~. ~ (3) n-2 (2) n-l 50 (4) n-3 12Pj221j31 143. Given Yo, Yl. Y2. Y3 corresponding to values xo, XI' x 2 X3 for function Y -'= [(xl. a 0:;: x ::;; b. Let fix) is a polynomial of degree 3. Then by Simpson's three-eight rule J ~ J: fix) dx i$ 3 8 (1) J~-hIYo +3y, +3Y2 +Y3] (4) None of the above 1 (2) J=-hIYo +4Yl +Y2] 3 1 (3) J=-hI2yo +4Yl +2Y21 3 144. The value of bon (ax n + bx n:- 1 + c) is (1) 145. n' (2) an! Ii the observed values of x and function x 2 6 8 9 198 150 102 93 The interpolating function (347) (3) (n-1)! 3 -4x 2 (1) x {3J x 3 -18x 2 +80x+102 Ux (4) b(n-l)! are U)( IS +80x+l02 (2) x 3 -18x 2 +80x+294 {4} None of the above 51 (P. T. D.) 12P/221/31 x 146. 2 6 8 9 198 150 102 93 (1) x 3 _4x 2 +80x+l02 (3) x 3 -18x' +80x+102 (2) In Picard's method, given initial value problem y' nth approximation (1) Yn =yo+I x x" ~ dy ~ fix, y) with ylxo) ~Yo dx ~s (2) Yn f{x,xn)dx (3) Yn ~ Yo + IX fix, Yn-Ji dx x" y' ~ dy ~ fix, dx ~ Yo + IX fix, y) dx x" (4) None of the above y) with ylxo) i2I' (3) Yn ~Yo+Ix flx,Yn_Jidx x" (347) x 3 -18x 2 +80x+294 52 Yn ~ Yo ~ Yo + J: fix, y)dx 1.2P{221{31 147. Parabolic method Of estimation is good for (1) interpolation (2) extrapolation (3) interpolation as well as extrapolation (4) None of the above ~ <lit ".eft. fOfu ~ ~, - - ~ ~I (1) 'Hl~'1'! (3) ",.. 4.1. l!1>I-"WI 148.. Degree of freedom for chi-square in case of conti:Qgency table of order (4x3) is (1) 1.. .~4". 12 (3) 8 (2) 9 A random sample (X" X 2, X 3) (4) 6 is drawn from U(O,S). Let T 'pen to be unbiased for 8, then the value of a is u(o,a) il (X"X 2 'X 3 ) ""' <lI<;R>.. ~ ~11l1'! <'f ill; T=3X1 +2X ., 2 .+aX 3 . ~ iM ~ ~ ~, (II 1 150. <it a,," 1l1'! .rm (3) 0 (2) 5 (4) 2 If the characteristic function of a discrete random variable X is {~+ j eit }; i == r-I, dIcn X is a (l~ Bernoulli variate (2) Poisson variate Pt normal variate (347) (4) negative binomial variate 53 (P.T.D.) 12P/221/31 ( 1) -..if<oI\ (3) ilr<R ,.,", .. ~ (2) ilr<R i "'lim ilr<R i (4) ""II," .. Ji:q<; ilr<R i *** 54 D/2(347)-400 1. *' *' ~ flI&.\ iii 10 fIR?: iii "'R" ~ ~1lI "# f<!; ~ if <1m 1"" >I1"l1; ~ 3i'n: q;]~ ;@ ~ I ~ ~ ~ -.rf.\ 'R ~ ~ ""'"'" 'li1a-f.rttPJ'!> q;] ~ ~ ~ <lit W1 ~ ~~ 3. WlT '1'!1 't, ;# , "lit ~""i", fiIr'lf """'" I "'"- 'l'! 3lWl " tt 'lW W 4. 3l'R1 JIj,""i.. 5. ""'-'l'!"o; ~'l'! "fIT "if'ir(-'lW ailo 1('10 amo 3ljt;tilOli<+i ~o 7. ~ "f.fu4f " -.m 'l'! '" am: 'IT# ""' , tt ~ <j;f I 'iJIl7 ~ JP!'l 0ll'I['l-'!lI 'If W "if'ir(- *' " f.r'llfu! 'lW WI' Iim..".q"" <"lR 'R i/;<m"if'ir(- WM' "''1iMi .. f.r'llfu! <"lR '" WM "'" oft-;! ~ '!'if qi\ "'"" '"' ~, ...,-~ ..rz "" "'" <!f\rn """ '" WM' it-! " 'j1! '" ;;r;i-;;r;i "',..... 1ft 6. "# I "SIll! "" 3l'R1 "" -'"' "'" "''1',"i .. <i=, ...,-:!fum <i= .. ..rz <i= ("""' afro ~o 3ffio -q3{ -Bo ~ ~ m m~ _ if f.rtllll'l' &m WlTfUrn dqf{f;{ ""l m m) "'" --:!fum 'R Cfl't ~ 1@ ~ I mon ~ il"Pl'" 'ffi "'" ~ m'R <>iT >!'1'r>! 'lR1 "'"""' 8. --:!fum" """"..., 'Iff ~ Wi> </; ""'" WI ~ '1" 'Iff 'lW "0; "'" "0; jffi """" _ 'f'I qi\ 1 O. ~ 'lW </; JP!'l 4.. R-... "if'ir( </; fi7>I >moil WI ~ fmif </; iffJfIT' JrFf </; '!lI 'If *' " '"'" 3l1:"f '1B "' % ~ "'" m'f'I qi\ "'"" ~, "'" " an"", '!'if qi\ "'"" "if'ir(- <rn "' "'''''' "'" "'" ""'" 'lR1 "'"""' ~ f'I; "'" om ~ &m ~ "'" <lGffi 'lliI "IT """" 't, """' 3IT'l f.l;B\ ..., <>iT "if'ir( 1(( t-rr ..mt --r"", m.. "0; m'f'I ~ "" <1m '!'if qi\ 1lITffi -.it9 ~, V:ll """ '" 'If'! ojq; ~ ~, UIR II: "if'ir(- '1', tl 'IR'/T 9. "0; "" ~ ..F~q .. "'" ~ "" <IT 11. "f -..rl "0; jffi _-~ "0; :Jl9'j1! "0; OR! """ 12. W'<lT"O; """'" ~ 13. W'<lT 14. """' ",,,,off W'<lT " ~ m'R'! "" >!'1'r>! ""'" iPTI!li\>i\ , wm! m oito1('fo,,",o "if'ir(-'lW 'j1! "'" aifuq 'j1! "" >!'1'r>! ~, W'<lT """ " """ '"' ~, 1if.I " 'l1'<"t W'<lT """ " """ "'!f.\ qi\ 3lJ'lfu 'lliI jfrft, t <IT % f f .,,,. &m f.r'llfu! ~ "",.;t, 'Wil

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