Download DUET Master 2018 DU MA MSc Statistics Question Paper With Answer Key

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DU MA MSC Statistics

Topic:- DU_J18_MA_STATS_Topic01

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1. In analysis of variance problem involving 3 treatments with 10 observations each, SSE= 399.6. Then the MSE is equal to: [Question ID = 2313]
   1. 14.8 [Option ID = 9252]
   2. 133.2 [Option ID = 9249]
   3. 30 [Option ID = 9251]
   4. 13.32 [Option ID = 9250]

   Correct Answer :-

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   14.8 [Option ID = 9252]

2. If the variability due to chance decreases, the value of F: [Question ID = 2309]
   1. Decreases [Option ID = 9234]
   2. Stay the same [Option ID = 9235]
   3. Increases [Option ID = 9233]

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   4. Nothing can be said from given information [Option ID = 9236]

   Correct Answer :-

   Increases [Option ID = 9233]

3. If an unbiased coin is flipped till a first Head occurs, then the sample space is: [Question ID = 2284]
   1. {H,TH} [Option ID = 9135]

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   2. {H,TH,TTH,TTTH,....} [Option ID = 9136]
   3. {TH} [Option ID = 9134]
   4. {H} [Option ID = 9133]

   Correct Answer :-

   {H,TH,TTH,TTTH,....} [Option ID = 9136]

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4. The listing of elements in population with distinct identifiable number is classified as: [Question ID = 2305]
   1. Regularity experimental frame [Option ID = 9219]
   2. Frame for experiment [Option ID = 9220]
   3. Direct experimental frame [Option ID = 9217]
   4. Indirect experimental frame [Option ID = 9218]

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   Correct Answer :-

   Frame for experiment [Option ID = 9220]

5. When there is rough linearity between the principal variable Y and the auxiliary variable X, but there is no proportionality, the link between Y and X can be exploited to improve simple random sample estimator by using: [Question ID = 2307]
   1. Both Ratio estimator and Regression estimator [Option ID = 9227]
   2. Combined estimator [Option ID = 9228]

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   3. Regression estimator [Option ID = 9226]
   4. Ratio estimator [Option ID = 9225]

   Correct Answer :-

   Regression estimator [Option ID = 9226]

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6. In LSD with 5 treatments and one missing plot, the error degrees of freedom is: [Question ID = 2310]
   1. 15 [Option ID = 9238]
   2. 11 [Option ID = 9239]
   3. 12 [Option ID = 9240]
   4. 16 [Option ID = 9237]

   Correct Answer :-

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   11 [Option ID = 9239]

7. In the context of characteristic function of a random variable, which one of the following statements is false? [Question ID = 2293]
   1. It always exists. [Option ID = 9169]
   2. It is uniformly continuous on R. [Option ID = 9170]
   3. It is not independent of change of origin and scale. [Option ID = 9171]

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   4. If characteristic function of sum of two random variables is same as the product of their individual characteristic functions, then the variables are independent. [Option ID = 9172]

   Correct Answer :-

   If characteristic function of sum of two random variables is same as the product of their individual characteristic functions, then the variables are independent. [Option ID = 9172]

8. The area under a normal curve between one standard deviation on either side of the mean is: [Question ID = 2285]
   1. 95% [Option ID = 9138]

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   2. 68% [Option ID = 9139]
   3. 60% [Option ID = 9140]
   4. 99% [Option ID = 9137]

   Correct Answer :-

   68% [Option ID = 9139]

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9. In case of two attributes A and B if (A) = 30, (B) = 40, N = 200, then for A and B to be negatively associated the frequency of the class AB will be: [Question ID = 2289]
   1. 0 < (AB) < 6 [Option ID = 9155]
   2. (AB) = 6 [Option ID = 9154]
   3. (AB) = 0 [Option ID = 9153]
   4. (AB) > 6 [Option ID = 9156]

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   Correct Answer :-

   0 < (AB) < 6 [Option ID = 9155]

10. Suppose that there is a chance for a newly constructed building to collapse, whether the design is faulty or not. The chance that the design is faulty is 10%. The chance that the building collapses is 95% if the design is faulty and otherwise it is 45%. If it is seen that the building has collapsed, then the probability that it is due to faulty design is: [Question ID = 2277]
    1. 0.95 [Option ID = 9108]
    2. 0.19 [Option ID = 9106]

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    3. 0.45 [Option ID = 9107]
    4. 0.1 [Option ID = 9105]

    Correct Answer :-

    0.19 [Option ID = 9106]

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11. If ANOVA procedure is applied to the data obtained from 5 samples, where each sample contains 9 observations, then the degrees of freedom for critical value of F are: [Question ID = 2312]
    1. 5 and 9 [Option ID = 9245]
    2. 4 and 44 [Option ID = 9247]
    3. 4 and 40 [Option ID = 9248]
    4. 4 and 8 [Option ID = 9246]

    Correct Answer :-

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    4 and 40 [Option ID = 9248]

12. The ages of 7 family members are 2, 5, 12, 18, 38, 40 and 60 years respectively. After 5 years a new member aged x years is added. If the mean age of the family now goes up by 1.5 years, then the value of x (in years) is: [Question ID = 2287]
    1. 2 [Option ID = 9146]
    2. 1 [Option ID = 9145]
    3. 3 [Option ID = 9147]

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    4. 4 [Option ID = 9148]

    Correct Answer :-

    2 [Option ID = 9146]

13. Consider the 2³ factorial experiment in blocks of 4 plots, involving three fertilizers N, P, and K each at two levels.

    	Replicate I	Replicate II	Replicate III
    Block 1	np, npk,(1),k	pk, nk, (1), np	(1), npk, nk, p
    Block 2	p, n, pk, nk	np, npk, p, k	n, npk, p,k

    [Question ID = 2311]
    1. NK, NPK, PK [Option ID = 9244]

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    2. PK, NPK,PN [Option ID = 9243]
    3. NP, NK, PK [Option ID = 9241]
    4. NP, NPK, NK [Option ID = 9242]

    Correct Answer :-

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14. An urn contains 3 white and 4 black balls. A ball is drawn at random, its colour is noted and returned to urn along with two additional balls of the same colour. If a ball is drawn again from the urn, then the probability that the ball drawn is white, is: [Question ID = 2274]
    1. 5/9 [Option ID = 9094]
    2. 3/19 [Option ID = 9093]
    3. 3/7 [Option ID = 9095]
    4. 4/7 [Option ID = 9096]

    Correct Answer :-

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    3/7 [Option ID = 9095]

15. Let A = (a_ij), where a_ij =

    1,	i + j, is even
    -1	i + j, is odd

    be a square matrix of order 2k×2k and B be a column vector of order 2k x 1 with all elements as unity. Then the value of B'AB is: [Question ID = 2273]
    1. 0 [Option ID = 9089]
    2. 2k^-1 [Option ID = 9091]
    3. 4k² [Option ID = 9092]

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    4. 2k² [Option ID = 9090]

    Correct Answer :-

16. Let X be a single observation from truncated Poisson distribution having probability mass function P(X = x) = e^-?/x!(1-e^-?); x = 1, 2, 3, . The estimator T =

    2,	x = 1,3,5,...
    0,	x = 2,4,6,...

    is unbiased for: [Question ID = 2302]
    1. (1+e^-?)/(1-e^-?) [Option ID = 9208]
    2. (1-e^-?)/(1-e^-2?) [Option ID = 9205]

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    3. (1-e^-?)/(1-2e^-?) [Option ID = 9206]
    4. (1-e^-?)/(1-e^-2?) [Option ID = 9207]

    Correct Answer :-

    (1+e^-?)/(1-e^-?) [Option ID = 9208]

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17. If v_r is the absolute moment of order r about origin zero of a distribution, then: [Question ID = 2281]
    1. v_r² = v_r-1v_r+1 [Option ID = 9121]
    2. none of the above [Option ID = 9124]
    3. v_r² <= v_r-1v_r+1 [Option ID = 9122]
    4. v_r² >= v_r-1v_r+1 [Option ID = 9123]

    Correct Answer :-

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    v_r² >= v_r-1v_r+1 [Option ID = 9123]

18. Suppose that the five random variables X₁,X₂,..., X₅ are independent and each has standard normal distribution. A constant C such that the random variable C(X₁+X₂)/(X₃² + X₄² + X₅²)^½ will have a t-distribution has value: [Question ID = 2283]
    1. 3/2 [Option ID = 9131]
    2. 3/v2 [Option ID = 9130]
    3. v3/2 [Option ID = 9132]

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    4. v3/v2 [Option ID = 9129]

    Correct Answer :-

    3/v2 [Option ID = 9130]

19. The two candidates A and B for the presidentship of a Students' Union were asked to rank 4 issues in the order of their perceived importance. Their responses are listed besides the issues.

    ISSUE	Ranking by candidates
    	A	B
    Crime against girl students	1	2
    Corruption in sports	4	3
    Education system	3	4
    Unemployment	2	1

    Based on this data, Spearman's Rank Correlation Coefficient is: [Question ID = 2291]
    1. 1/5 [Option ID = 9161]

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    2. 3/5 [Option ID = 9163]
    3. 4/5 [Option ID = 9164]
    4. 2/5 [Option ID = 9162]

    Correct Answer :-

    3/5 [Option ID = 9163]

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20. If A is non-singular matrix of order 4x4 and determinant of Adj(A) is 4 then the value of 2Adj(3A) is: [Question ID = 2269]
    1. (3v2)¹² [Option ID = 9074]
    2. (2v2)¹² [Option ID = 9073]
    3. 3¹² [Option ID = 9075]
    4. 2¹² [Option ID = 9076]

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    Correct Answer :-

    (3v2)¹² [Option ID = 9074]

21. Nine elements of which 4 are of one kind and 5 are of a different kind are arranged in a sequence. If R is the number of runs, then P(R=2) is equal to: [Question ID = 2280]
    1. 1/126 [Option ID = 9118]
    2. 1/63 [Option ID = 9117]

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    3. 1/56 [Option ID = 9119]
    4. 1/42 [Option ID = 9120]

    Correct Answer :-

    1/63 [Option ID = 9117]

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22. Let X be a random variable with probability density function f? (f₀, f₁), where f₀(x) =

    2x,	0<x<1
    0,	otherwise.

    f₁(x) =

    4x3,	0<x<1
    0,	otherwise.

    and W = {x: x > c} is the rejection region for testing null hypothesis H₀: f = f₀ against H₁ : f = f₁, with level of significance a. Then power of the most powerful test is: [Question ID = 2298]
    1. a -2a² [Option ID = 9191]
    2. 2a-a² [Option ID = 9189]
    3. 2(a-a²) [Option ID = 9192]
    4. a - a² [Option ID = 9190]

    Correct Answer :-

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    2a-a² [Option ID = 9189]

23. The estimator T_o is MVU estimator for ?(?) and T₁ is any other unbiased estimator for ?(?) with efficiency 0.0169, then correlation between T_o and T₁ is: [Question ID = 2300]
    1. 0.013 [Option ID = 9197]
    2. 0.5 [Option ID = 9200]
    3. 0.13 [Option ID = 9198]

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    4. 0.0169 [Option ID = 9199]

    Correct Answer :-

    0.13 [Option ID = 9198]

24. Let X follows exponential distribution with mean ?. For testing the null hypothesis H_o: ? = 3 against H₁: ? = 5, a test gives rejection region W = {x, x = 4.5}. The size of the type - II error is: [Question ID = 2299]
    1. e^-20 [Option ID = 9196]

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    2. 1-e^-20 [Option ID = 9194]
    3. 1-e^-4.5 [Option ID = 9193]
    4. e^-9/2 [Option ID = 9195]

    Correct Answer :-

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25. The area enclosed by curves y² = x, y² = 3x-1 where 0 = x = ½ is: [Question ID = 2267]
    1. v2/3 [Option ID = 9066]
    2. 2v2/9 [Option ID = 9068]
    3. 2/9 [Option ID = 9065]
    4. v2/9 [Option ID = 9067]

    Correct Answer :-

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    v2/9 [Option ID = 9067]

26. If A is a 3x3 matrix with Given values - 1,0 and 1 then value of 6|A| is: [Question ID = 2265]

    1. -1	5	2
       5	-1	2
       2	2	2

       [Option ID = 9060]

    2. 1	5	3
       5	1	3
       3	1	5

       [Option ID = 9058]

    3. 1	0	0
       0	-1	4
       0	0	1

       [Option ID = 9059]

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    4. -3	9	0
       9	-3	0
       0	0	7

       [Option ID = 9057]

    Correct Answer :-

27. Let X₁ = 2.4, X₂ = 9.2, x₃ = 5.2, x₄ = 4.1, x₅ = 2.1 and x₆ = 3.1 be the observed values of a random variable of size 6 from uniform distribution with parameters (?-2, ?+6) where ? 0 is unknown, then MLE of ? is: [Question ID = 2295]
    1. 3.5 [Option ID = 9178]
    2. 4.5 [Option ID = 9179]

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    3. 9.2 [Option ID = 9180]
    4. 2.5 [Option ID = 9177]

    Correct Answer :-

    3.5 [Option ID = 9178]

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28. Let X₁, X₂,..., X_n be a random sample from Cauchy distribution with location parameter ? and scale parameter 1. The Cramer Rao lower bound for unknown parameter ?, is: [Question ID = 2303]
    1. 2/n [Option ID = 9212]
    2. 4/n [Option ID = 9211]
    3. 1/n [Option ID = 9209]
    4. 3/n [Option ID = 9210]

    Correct Answer :-

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    2/n [Option ID = 9212]

29. Suppose that p(x, y), the joint probability mass function (p.m.f.) of discrete random variables X and Y, is given by: p(0,0) = 0.4, p(0,1) = 0.2, p(1,0) = 0.1, p(1,1) = 0.3. Then the conditional p.m.f. of X, given that Y=1, is: [Question ID = 2290]
    1. P_X|Y(0|1) = 3/2, P_X|Y(1|1) = 3/2 [Option ID = 9160]
    2. P_X|Y(0|1) = 3/5, P_X|Y(1|1) = 3/5 [Option ID = 9157]
    3. P_X|Y(0|1) = 4/5, P_X|Y(1|1) = 3/5 [Option ID = 9158]

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    4. P_X|Y(0|1) = 1/5, P_X|Y(1|1) = 2/5 [Option ID = 9159]

    Correct Answer :-

    P_X|Y(0|1) = 1/5, P_X|Y(1|1) = 2/5 [Option ID = 9157]

30. The frequency distribution of percentage of marks obtained by a group of 229 students is given below with two missing frequencies marked as f₁ and f₂:

    Percentage of marks	No. of students	Percentage of marks	No. of students
    10-20	12	50-60	f2
    20-30	30	60-70	25
    30-40	f1	70-80	18
    40-50	65

    If the median of the distribution is 46, then the missing values of f₁ and f₂ are: [Question ID = 2278]
    1. f₁ = 34, f₂ = 45 [Option ID = 9109]

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    2. f₁ = 8, f₂ = 71 [Option ID = 9111]
    3. f₁ = 40, f₂ =39 [Option ID = 9112]
    4. f₁ = 66, f₂ = 13 [Option ID = 9110]

    Correct Answer :-

    f₁ = 34, f₂ = 45 [Option ID = 9109]

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31. The equation whose roots are cubes of roots of equation x³ - x = 0 is: [Question ID = 2266]
    1. x³ - 9x = 0 [Option ID = 9061]
    2. x³ + x = 0 [Option ID = 9063]
    3. x³ - x = 0 [Option ID = 9064]
    4. x³ + x² + x - 1 = 0 [Option ID = 9062]

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    Correct Answer :-

    x³ - x = 0 [Option ID = 9064]

32. Let X₁, X₂,..., X_n be a random sample of size n from N(?₁, ?₂), then the estimate of (?₁, ?₂) using the method of moments is: [Question ID = 2296]
    1. ?₁ = 1/n SX_i, ?₂ = 1/2n S(X_i-X)² [Option ID = 9183]
    2. ?₁ = 1/n SX_i, ?₂ = 1/n S(X_i-X)² [Option ID = 9182]

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    3. ?₁ = 1/n SX_i, ?₂ = 1/2n-1 S(X_i-X)² [Option ID = 9184]
    4. ?₁ = 1/n SX_i, ?₂ = 1/n-1 S(X_i-X)² [Option ID = 9181]

    Correct Answer :-

33. If the observations recorded on five sampled items are 3, 4, 5, 6, 7, then the unbiased estimate of the population variance is: [Question ID = 2276]
    1. 0 [Option ID = 9101]

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    2. 1 [Option ID = 9102]
    3. 2 [Option ID = 9103]
    4. 2.5 [Option ID = 9104]

    Correct Answer :-

    2.5 [Option ID = 9104]

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34. The equation of tangents at origin to the curve x² (a² - x²) = y² (a² + x²) is: [Question ID = 2271]
    1. y = ±ax [Option ID = 9084]
    2. y = ±x [Option ID = 9083]
    3. x = ±ay [Option ID = 9081]
    4. y = ±2x [Option ID = 9082]

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    Correct Answer :-

    y = ±x [Option ID = 9083]

35. An urn contains 5 red and 3 black balls. Balls are drawn, one-by-one, with replacement till the 3^rd red ball is drawn. The probability that 3^rd red ball occurs at the 5^th draw is: [Question ID = 2292]
    1. 5³/8⁵ [Option ID = 9168]
    2. 6.5³.3²/8⁵ [Option ID = 9165]

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    3. 5³.3²/8⁵ [Option ID = 9166]
    4. 6.5³/8⁵ [Option ID = 9167]

    Correct Answer :-

    6.5³.3²/8⁵ [Option ID = 9165]

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36. The slope of tangents at double point (x, y) to the curve f(x,y) = 0 is given by solution of the quadratic equation: [Question ID = 2272]
    1. (?²f/?x²)(dy/dx)² + (?²f/?x?y)(dy/dx) + (?²f/?y²) = 0 [Option ID = 9087]
    2. (?²f/?y²)(dy/dx)² + 2(?²f/?x?y)(dy/dx) + (?²f/?x²) = 0 [Option ID = 9088]
    3. (?²f
       

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