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Topic:- STATS MPHIL S2

1. A fraction non-conforming control chart with n=400 has the following parameters; UCL=0.0809, CL=0.05, LCL=0.0191. The corresponding parameters for an equivalent control chart based on the number non conforming are

   [Question ID = 4266]

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   1. (5.92, 32.08) [Option ID = 17058]
   2. (6.92, 33.08) [Option ID = 17059]
   3. (7.92, 34.08) [Option ID = 17060]
   4. (8.92, 35.08) [Option ID = 17061]

   Correct Answer :-

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   • (6.92, 33.08) [Option ID = 17059]

2. In an abridged life table, functions are computed for

   [Question ID = 4267]

   1. Each year of age [Option ID = 17062]

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   2. Age intervals greater than one year [Option ID = 17063]
   3. From birth till the death of last member of the group [Option ID = 17064]
   4. None of these [Option ID = 17065]

   Correct Answer :-

   • Age intervals greater than one year [Option ID = 17063]

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3. Suppose that a parallel system with identical components has an overall reliability of 0.98. If each component has reliability of 0.25, then the minimum number of components in the system will be

   [Question ID = 4268]

   1. 12 [Option ID = 17066]
   2. 13 [Option ID = 17067]

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   3. 14 [Option ID = 17068]
   4. 15 [Option ID = 17069]

   Correct Answer :-

   • 14 [Option ID = 17068]

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4. The reliability of a series system decreases with

   [Question ID = 4269]

   1. A decrease in the number of its components [Option ID = 17070]
   2. An increase in the number of its components [Option ID = 17071]
   3. Same number of its components [Option ID = 17072]

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   4. None of these [Option ID = 17073]

   Correct Answer :-

   • An increase in the number of its components [Option ID = 17071]

5. If a manufacturing process produces a large number of non-conforming units, then the process capability is

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   [Question ID = 4270]

   1. Less than one [Option ID = 17074]
   2. Greater than one [Option ID = 17075]
   3. Equal to one [Option ID = 17076]
   4. Equal to zero [Option ID = 17077]

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6. Octal equivalent of binary number 1100000 is:

   [Question ID = 4271]

   1. 192 [Option ID = 17078]
   2. 300 [Option ID = 17079]

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   3. 071 [Option ID = 17080]
   4. 301 [Option ID = 17081]

   Correct Answer :-

   • 300 [Option ID = 17079]

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7. Converted value of (53)₈ to Base 10 is :

   [Question ID = 4272]

   1. 43 [Option ID = 17082]
   2. 63 [Option ID = 17083]
   3. 64 [Option ID = 17084]

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   4. 42 [Option ID = 17085]

   Correct Answer :-

   • 43 [Option ID = 17082]

8. Researches that are being conducted to study the Novel Coronavirus will be termed as:

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   [Question ID = 4273]

   1. action research [Option ID = 17086]
   2. applied research [Option ID = 17087]
   3. longitudinal research [Option ID = 17088]
   4. empirical research [Option ID = 17089]

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   Correct Answer :-

   • action research [Option ID = 17086]

9. Ex post facto research refers to :

   [Question ID = 4274]

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   1. descriptive research [Option ID = 17090]
   2. fundamental research [Option ID = 17091]
   3. analytical research [Option ID = 17092]
   4. empirical research [Option ID = 17093]

   Correct Answer :-

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   • descriptive research [Option ID = 17090]

10. The applied research uses the principles of :

    [Question ID = 4275]

    1. Action research [Option ID = 17094]

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    2. Fundamental research [Option ID = 17095]
    3. Philosophical research [Option ID = 17096]
    4. Historical research [Option ID = 17097]

    Correct Answer :-

    • Fundamental research [Option ID = 17095]

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11. Regarding earthquake as a rare phenomenon with the occurrence rate of 2 per week, the probability that at least 3 earthquakes occur during the next 2 weeks is www.FirstRanker.com

    [Question ID = 4276]

    1. 1-12e^-4 [Option ID = 17098]

    Correct Answer :-

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    • 12e^-4 [Option ID = 17098]

12. The number of marriages that remain intact when there are a total of m deaths among the N married couples are

    [Question ID = 4277]

    1. {(2N-m) (2N-m+2) }/ (2N-1) [Option ID = 17102]

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    2. {(2N-m) (2N-m-1)}/ (2N-1) [Option ID = 17103]
    3. {2(2N-m) (2N-m-1)}/ (2N-1) [Option ID = 17104]
    4. {(2N-m) (2N-m-1)}/{2 (2N-1)} [Option ID = 17105]

    Correct Answer :-

    • {(2N-m) (2N-m-1)}/{2 (2N-1)} [Option ID = 17105]

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13. The expected sum obtained when 10 independent rolls of a fair dice are made is

    [Question ID = 4278]

    1. 20 [Option ID = 17106]
    2. 30 [Option ID = 17107]

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    3. 35 [Option ID = 17108]
    4. 45 [Option ID = 17109]

    Correct Answer :-

    • 35 [Option ID = 17108]

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14. Ten hunters randomly fire at a swarm of birds flying overhead. Assume that each hunter acts independently and that each hunter hits the target with probability p. The expected number of birds that escape unhurt when a flock of size 10 flies overhead is

    [Question ID = 4279]

    1. 100(1-p/10) [Option ID = 17110]
    2. [10-(p/10)]¹⁰ [Option ID = 17111]
    3. 10(1-p/10)¹⁰⁰ [Option ID = 17112]

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    4. 10(1-p/10)¹⁰ [Option ID = 17113]

    Correct Answer :-

    • 10(1-p/10)¹⁰ [Option ID = 17113]

15. Given the fundamental matrix M = $\left[\begin{array}{c}\frac{5}{4}\frac{3}{2}\\ \frac{1}{2}& \frac{3}{2}\end{array}\right]$ and the submatrix R of the one-step transition probability matrix, which represents transitions from the transient states to the absorbing states such that R = $\left[\begin{array}{cc}\frac{1}{2}& 0\\ 0& \frac{1}{2}\end{array}\right]$ , determine a₃₅ the absorption probability a_ij where a_ij for i = 2,3,4 and j = 4,5 .

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    [Question ID = 4280]

    1. 5/8 [Option ID = 17114]
    2. 1/4 [Option ID = 17115]
    3. 3/4 [Option ID = 17116]
    4. 15/16 [Option ID = 17117]

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    Correct Answer :-

    • 3/4 [Option ID = 17116]

16. In estimating simultaneous equation models by indirect least squares method, which of the following is true?

    [Question ID = 4281]

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    1. GLS is applied to the reduced form equation [Option ID = 17118]
    2. GLS is applied to the structural equation [Option ID = 17119]
    3. OLS is applied to the reduced form equation [Option ID = 17120]
    4. OLS is applied to the structural equation [Option ID = 17121]

    Correct Answer :-

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    • OLS is applied to the reduced form equation [Option ID = 17120]

17. Which of the following is NOT a consequence of the presence of heteroscedasticity in a linear regression model?

    1. As a consequence of error-learning models [Option ID = 17122]
    2. Use of data manipulation techniques like data smoothing, interpolation, extrapolation, imputation etc. [Option ID = 17123]

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    3. Incorrect specification of the functional form of the model [Option ID = 17124]
    4. Incorrect transformation of variables [Option ID = 17125]

    Correct Answer :-

    • Use of data manipulation techniques like data smoothing, interpolation, extrapolation, imputation etc. [Option ID = 17123]

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18. While fitting a linear regression model with intercept, using ordinary least squares estimation, the value of Durbin- Watson d statistic came out to be 0. What does it signify?

    [Question ID = 4283]

    1. Autocorrelation is not present in the disturbances [Option ID = 17126]
    2. Autocorrelation is not present in the independent variables [Option ID = 17127]
    3. Heteroscedasticity is not present in the model [Option ID = 17128]

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    4. Evidence of positive autocorrelation of order 1 in the disturbances [Option ID = 17129]

    Correct Answer :-

    • Evidence of positive autocorrelation of order 1 in the disturbances [Option ID = 17129]

19. Consider the following linear regression model,

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    Y_i = β₀+β₁X_1i+β₂X_2i + β₃X_3i + U_i

    To test the presence of multicollinearity, we calculate pair-wise correlation coefficients between X₁, X₂, and X₃. Then, high pair-wise correlation coefficients can be treated as

    [Question ID = 4284]

    1. A necessary condition but not a sufficient condition for high multicollinearity [Option ID = 17130]
    2. Both a necessary and a sufficient condition for high multicollinearity [Option ID = 17131]

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    3. Neither necessary nor sufficient for presence of high multicollinearity [Option ID = 17132]
    4. A sufficient condition but not a necessary condition for high multicollinearity [Option ID = 17133]

    Correct Answer :-

    • A sufficient condition but not a necessary condition for high multicollinearity [Option ID = 17133]

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20. Which one of the following critical classical assumptions of least squares estimation of linear regression models does the Koyck transformation (for distributed lag models) not satisfy?

    [Question ID = 4285]

    1. The values of the explanatory variables are non-stochastic [Option ID = 17134]
    2. The regression model is correctly specified [Option ID = 17135]
    3. There is no perfect linear relationship between the explanatory variables [Option ID = 17136]

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    4. The number of observations must be greater than the number of explanatory variables [Option ID = 17137]

    Correct Answer :-

    • The values of the explanatory variables are non-stochastic [Option ID = 17134]

21. 21) Which of the following relation among modes of convergence is true?

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    [Question ID = 4286]

    1. $\stackrel{P}{X_n}\to X$ [Option ID = 17138]
    2. $\stackrel{d}{X_n}\to X$ [Option ID = 17139]
    3. $\stackrel{th}{X_n}\to X$ [Option ID = 17140]
    4. $\stackrel{P}{X_n}\to X$ [Option ID = 17141]

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    Correct Answer :-

    • $\stackrel{th}{X_n}\to X$ [Option ID = 17140]

22. The necessary and sufficient condition for WLLN to hold for the arbitrary sequence of random variables {X_n} is

    [Question ID = 4287]

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    1. Variance should exist. [Option ID = 17142]
    2. lim B_n = 0 where, B_n = Var(X₁ + X₂ + ... + X_n) $\underset{n\to \mathrm{\infty }}{lim}\frac{B_n}{n^2}=0$ www.FirstRanker.com
    3. E(X_n) should exist [Option ID = 17145]

    Correct Answer :-

    • E(|X₁|^1+δ) exists for some δ > 0 [Option ID = 17144]

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23. Which of the following statement is correct about the sequence of i.i.d. Cauchy variates having p.d.f.

    f(x) = 1 / (π(1 + x²)), -∞ < x < ∞

    [Question ID = 4288]

    1. WLLN does not hold but CLT holds [Option ID = 17146]

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    2. CLT does not hold but WLLN holds [Option ID = 17147]
    3. Both WLLN and CLT do not hold [Option ID = 17148]
    4. Both WLLN and CLT hold [Option ID = 17149]

    Correct Answer :-

    • Both WLLN and CLT do not hold [Option ID = 17148]

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24. Let X_k,k = 1,2,..., n be pairwise independent random variables taking two values k and -k with equal probabilities. Choose the correct statement

    [Question ID = 4289]

    1. WLLN does not hold for the sequence {X_k} [Option ID = 17150]
    2. WLLN holds for the sequence {X_k} [Option ID = 17151]

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    3. WLLN holds if K=1 [Option ID = 17152]
    4. WLLN can not be examined [Option ID = 17153]

    Correct Answer :-

    • WLLN does not hold for the sequence {X_k} [Option ID = 17150]

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25. Let f(x,y) = e^-(x+y), 0 < x < 0,0 < y < ∞. The value of P[X < Y|X < 2Y] is

    [Question ID = 4290]

    1. 3/4 [Option ID = 17154]
    2. 1/4 [Option ID = 17155]
    3. 1/3 [Option ID = 17156]

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    4. 1 [Option ID = 17157]

    Correct Answer :-

    • 3/4 [Option ID = 17154]

26. Which of the following is NOT true?

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    www.FirstRanker.com

    [Question ID = 4291]

    1. Covariance matrix is a symmetric matrix [Option ID = 17158]
    2. Covariance matrix of X and X is a symmetric matrix [Option ID = 17159]
    3. Covariance matrix of X and Y is a square matrix [Option ID = 17160]
    4. Covariance matrix of X and Y is the transpose of covariance matrix of Yand X [Option ID = 17161]

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    Correct Answer :-

    • Covariance matrix of X and Y is a square matrix [Option ID = 17160]

27. If X~N_p(μ,Σ), then (X – μ)^TΣ^-1(X – μ) follows

    [Question ID = 4292]

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    1. Wishart distribution [Option ID = 17162]
    2. χ² distribution [Option ID = 17163]
    3. Hotelling's T² distribution [Option ID = 17164]
    4. None of these [Option ID = 17165]

    Correct Answer :-

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    • χ² distribution [Option ID = 17163]

28. If X~N₂(0,Σ), where Σ = $\left[\begin{array}{cc}1& \rho \\ \rho & 1\end{array}\right]$ . For what value of ρ, X₁ + X₂ and X₁ – X₂ are independent?

    [Question ID = 4293]

    1. 1 [Option ID = 17166]

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    2. 2 [Option ID = 17167]
    3. 0 [Option ID = 17168]
    4. -1 [Option ID = 17169]

    Correct Answer :-

    • 0 [Option ID = 17168]

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29. Which of the following technique helps to assign objects to one of the groups among a number of groups?

    [Question ID = 4294]

    1. Discriminant analysis [Option ID = 17170]
    2. Principal component analysis [Option ID = 17171]

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    3. Factor analysis [Option ID = 17172]
    4. None of these [Option ID = 17173]

    Correct Answer :-

    • Discriminant analysis [Option ID = 17170]

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30. If Y~N₃(μ, Σ), with μ = $\left[\begin{array}{c}2\\ mn1\\ 3\end{array}\right]$ Σ = $\left[\begin{array}{ccc}3& -2& 2\\ -2& 2& 1\\ 2& 1& 1.5\end{array}\right]$ then the joint distribution of Y₁, Y₂, and Y₃ = (Y₂ +Y₃) is www.FirstRanker.com

    1. N₃ $\left[\begin{array}{c}2\\ 1\\ 4\end{array}\right]$ $\left[\begin{array}{ccc}3& -2& 2\\ -2& 2& 1\\ 2& 1& 1.5\end{array}\right]$ [Option ID = 17174]
    2. N₃ $\left[\begin{array}{c}3\\ 3\\ 2.0\end{array}\right]$ $\left[\begin{array}{ccc}3& -2& 2.01\\ \mathrm{<p>This\; download\; link\; is\; referred\; from\; the\; post:\; <a\; href="https://firstranker.com/duet/duet-last-10-years-2010-2020-question-papers-with-answer-key-delhi-university-entrance-test-conducted-by-the-nta/">DUET\; Last\; 10\; Years\; 2011-2021\; Question\; Papers\; With\; Answer\; Key\; ||\; Delhi\; University\; Entrance\; Test\; conducted\; by\; the\; NTA</a></p>}\end{array}\right]$

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