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

Download DUET (Delhi University Entrance Test conducted by the NTA) 2018 DU MA MSc Statistics Question Paper With Solution Key

This post was last modified on 29 January 2020

Tags: DUET Delhi University Entrance Test NTA Master MA MSc Statistics Question Paper Answer Key 2018 PDF Download

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This download link is referred from the post: DUET Last 10 Years 2011-2021 Question Papers With Answer Key || Delhi University Entrance Test conducted by the NTA

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DU MA MSC Statistics

Topic:- DU_J18_MA_STATS_Topic01

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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]
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]
4. Nothing can be said from given information [Option ID = 9236]
Correct Answer :-

Increases [Option ID = 9233]
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]
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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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]
Correct Answer :-

Frame for experiment [Option ID = 9220]
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]
3. Regression estimator [Option ID = 9226]
4. Ratio estimator [Option ID = 9225]
Correct Answer :-

Regression estimator [Option ID = 9226]

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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]
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]
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]
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]
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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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]
Correct Answer :-

0 < (AB) < 6 [Option ID = 9155]
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]
3. 0.45 [Option ID = 9107]
4. 0.1 [Option ID = 9105]
Correct Answer :-

0.19 [Option ID = 9106]

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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]
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]
4. 4 [Option ID = 9148]
Correct Answer :-

2 [Option ID = 9146]
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]
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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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]
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]
4. 2k² [Option ID = 9090]
Correct Answer :-
Let X be a single observation from truncated Poisson distribution having probability mass function P(X = x) = e^-θ/x!(1-e^-θ); 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^-θ)/(1-e^-θ) [Option ID = 9208]
2. (1-e^-θ)/(1-e^-2θ) [Option ID = 9205]
3. (1-e^-θ)/(1-2e^-θ) [Option ID = 9206]
4. (1-e^-θ)/(1-e^-2θ) [Option ID = 9207]
Correct Answer :-

(1+e^-θ)/(1-e^-θ) [Option ID = 9208]

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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]
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/√2 [Option ID = 9130]
3. √3/2 [Option ID = 9132]
4. √3/√2 [Option ID = 9129]
Correct Answer :-

3/√2 [Option ID = 9130]
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]
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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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. (3√2)¹² [Option ID = 9074]
2. (2√2)¹² [Option ID = 9073]
3. 3¹² [Option ID = 9075]
4. 2¹² [Option ID = 9076]
Correct Answer :-

(3√2)¹² [Option ID = 9074]
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]
3. 1/56 [Option ID = 9119]
4. 1/42 [Option ID = 9120]
Correct Answer :-

1/63 [Option ID = 9117]

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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 α. Then power of the most powerful test is: [Question ID = 2298]
1. α -2α² [Option ID = 9191]
2. 2α-α² [Option ID = 9189]
3. 2(α-α²) [Option ID = 9192]
4. α - α² [Option ID = 9190]
Correct Answer :-
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2α-α² [Option ID = 9189]
The estimator T_o is MVU estimator for γ(θ) and T₁ is any other unbiased estimator for γ(θ) 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]
4. 0.0169 [Option ID = 9199]
Correct Answer :-

0.13 [Option ID = 9198]
Let X follows exponential distribution with mean θ. For testing the null hypothesis H_o: θ = 3 against H₁: θ = 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]
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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The area enclosed by curves y² = x, y² = 3x-1 where 0 ≤ x ≤ ½ is: [Question ID = 2267]
1. √2/3 [Option ID = 9066]
2. 2√2/9 [Option ID = 9068]
3. 2/9 [Option ID = 9065]
4. √2/9 [Option ID = 9067]
Correct Answer :-
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√2/9 [Option ID = 9067]
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]
4. -3 9 0
  
  9 -3 0
  
  0 0 7
  
  [Option ID = 9057]
Correct Answer :-
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 (θ-2, θ+6) where θ 0 is unknown, then MLE of θ is: [Question ID = 2295]
1. 3.5 [Option ID = 9178]
2. 4.5 [Option ID = 9179]
3. 9.2 [Option ID = 9180]
4. 2.5 [Option ID = 9177]
Correct Answer :-

3.5 [Option ID = 9178]

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Let X₁, X₂,..., X_n be a random sample from Cauchy distribution with location parameter θ and scale parameter 1. The Cramer Rao lower bound for unknown parameter θ, 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]
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]
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]
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]
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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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]
Correct Answer :-

x³ - x = 0 [Option ID = 9064]
Let X₁, X₂,..., X_n be a random sample of size n from N(θ₁, θ₂), then the estimate of (θ₁, θ₂) using the method of moments is: [Question ID = 2296]
1. θ₁ = 1/n ΣX_i, θ₂ = 1/2n Σ(X_i-X)² [Option ID = 9183]
2. θ₁ = 1/n ΣX_i, θ₂ = 1/n Σ(X_i-X)² [Option ID = 9182]
3. θ₁ = 1/n ΣX_i, θ₂ = 1/2n-1 Σ(X_i-X)² [Option ID = 9184]
4. θ₁ = 1/n ΣX_i, θ₂ = 1/n-1 Σ(X_i-X)² [Option ID = 9181]
Correct Answer :-
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]
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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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]
Correct Answer :-

y = ±x [Option ID = 9083]
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]
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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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
  This download link is referred from the post: DUET Last 10 Years 2011-2021 Question Papers With Answer Key || Delhi University Entrance Test conducted by the NTA

This post was last modified on 29 January 2020