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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]
   1. (5.92, 32.08) [Option ID - 17058]
   2. (6.92, 33.08) [Option ID - 17059]

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   3. (7.92, 34.08) [Option ID - 17060]
   4. (8.92, 35.08) [Option ID - 17061]
   Correct Answer :-
   • (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]
   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]
   4. None of these [Option ID - 17073]

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   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 [Question ID = 4270]
   1. Less than one [Option ID - 17074]
   2. Greater than one [Option ID - 17075]
   3. Equal to one [Option ID - 17076]

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   4. Equal to zero [Option ID - 17077]
6. Octal equivalent of binary number 1100000 is: [Question ID = 4271]
   1. 192 [Option ID - 17078]
   2. 300 [Option ID - 17079]
   3. 071 [Option ID - 17080]

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   4. 301 [Option ID - 17081]
   Correct Answer :-
   • 300 [Option ID - 17079]
7. Converted value of (53)8 to Base 10 is: [Question ID = 4272]
   1. 43 [Option ID - 17082]
   2. 63 [Option ID - 17083]

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   3. 64 [Option ID - 17084]
   4. 42 [Option ID - 17085]
   Correct Answer :-
   • 43 [Option ID - 17082]
8. Researches that are being conducted to study the Novle Coronavirus will be termed as: [Question ID = 4273]
   1. action research [Option ID - 17086]

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   2. applied research [Option ID - 17087]
   3. longitudinal research [Option ID - 17088]
   4. empirical research [Option ID - 17089]
   Correct Answer :-
   • action research [Option ID - 17086]

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9. Ex post facto research refers to : [Question ID = 4274]
   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 :-
   • descriptive research [Option ID - 17090]

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10. The applied research uses the principles of: [Question ID = 4275]
    1. Action research [Option ID - 17094]
    2. Fundamental research [Option ID - 17095]
    3. Philosophical research [Option ID - 17096]
    4. Historical research [Option ID - 17097]

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    Correct Answer :-
    • Fundamental research [Option ID - 17095]
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]
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]
    2. ((2N-m) (2N-m-1))/ (2N-1) [Option ID - 17103]

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    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]
13. The expected sum obtained when 10 independent rolls of a fair dice are made is [Question ID = 4278]
    1. 20 [Option ID - 17106]

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    2. 30 [Option ID - 17107]
    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)]¹° [Option ID - 17111]
    3. 10(1-p/10)¹°° [Option ID - 17112]
    4. 10(1-p/10)¹° [Option ID - 17113]
    Correct Answer:-
    • 10(1-p/10)¹° [Option ID - 17113]

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15. Given the fundamental matrix M = $\left(\begin{array}{cccc}\raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.\raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.& \raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.\raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.& \raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.\raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.& \raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.\raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.\\ \raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.\raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.& \raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.\raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.& \raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.\raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.& \raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.\raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.\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}\raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.\raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.& 0\\ 0& \raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.\raisebox{1ex}{$$}\!\left/ \!\raisebox{-1ex}{$$}\right.\\ 0& 0\end{array}\right)$ determine the absorption probability a? where a? for i = 2,3,4 and j = 4,5. [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]
    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]

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    4. OLS is applied to the structural equation [Option ID - 17121]
    Correct Answer :-
    • OLS is applied to the reduced form equation [Option ID - 17120]
17. Which of the following step / assumption in regression modeling impacts the trade-off between under-fitting and over fitting or 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]
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]

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    2. Autocorrelation is not present in the independent variables [Option ID - 17127]
    3. Heteroscedasticity is not present in the model [Option ID - 17128]
    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]

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19. Consider the following linear regression model, Y? = ß0 + ß1X1? + ß2X2? + ß3X3? + e? 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]
    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]
    4. The number of observations must be greater than the number of explanatory variables [Option ID - 17137]

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    Correct Answer :-
    • The values of the explanatory variables are non-stochastic [Option ID - 17134]
21. Which of the following relation among modes of convergence is true? [Question ID = 4286]
    1. X? ? X ^p
       ?
       X? ? X ^a.s. [Option ID - 17138]

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    2. X? ? X ^p
       ?
       X? ? X ^d [Option ID - 17139]
    3. X? ? X ^p
       ?
       

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       X? ? X ^d [Option ID - 17140]
    4. X? ? X ^p
       ?
       X? ? X ^d [Option ID - 17141]
    Correct Answer :-
    • X? ? X ^p
      

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      ?
      X? ? X ^d [Option ID - 17140]
22. The necessary and sufficient condition for WLLN to hold for the arbitrary sequence of random variables {X?} is [Question ID = 4287]
    1. Variance should exist. [Option ID - 17142]
    2. lim _n?8 B? = 0 where, B? = Var(X1 + X2 + ... + X?) [Option ID - 17143]

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    3. E(|X1|^1+d) exists for some d > 0 [Option ID - 17144]
    4. E(X?) should exist [Option ID - 17145]
    Correct Answer :-
    • E(|X1|^1+d) exists for some d > 0 [Option ID - 17144]
23. Which of the following statement is correct about the sequence of i.i.d. Cauchy variates having p.d.f. f(x) = 1/(p(1+x²)) -8 < x < 8 [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 = 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?} [Option ID - 17150]
    2. WLLN holds for the sequence {X?} [Option ID - 17151]
    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?} [Option ID - 17150]

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25. Let f(x,y)=(x+y),0 < x < 8,0 < y < 8. 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]
    4. 1 [Option ID - 17157]

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    Correct Answer :-
    • 3/4 [Option ID - 17154]
26. Which of the following is NOT true? [Question ID = 4291]
27. If X and Y are random variables then which of the following is true? [Question ID = 4291]
    1. Covariance matrix of X and Y is a square matrix [Option ID - 17159]
    2. Covariance matrix of X and Y is the transpose of covariance matrix of Y and X [Option ID - 17161]

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    Correct Answer :-
    • Covariance matrix of X and Y is a square matrix [Option ID - 17160]
28. If X ~ N?(µ, S), then (X - µ)?S?¹(X - µ) follows [Question ID = 4292]
    1. Wishart distribution [Option ID - 17162]
    2. ?² distribution [Option ID - 17163]
    3. Hotelling's T² distribution [Option ID - 17164]

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    4. None of these [Option ID - 17165]
    Correct Answer :-
    • ?² distribution [Option ID - 17163]
29. If X ~ N2(0, S), where S = $\left(\begin{array}{cc}1& ?\\ ?& 1\end{array}\right)$ For what value of ?, X1 + X2 and X1 - X2 are independent? [Question ID = 4293]
    1. 1 [Option ID - 17166]
    2. 2 [Option ID - 17167]

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    3. 0 [Option ID - 17168]
    4. -1 [Option ID - 17169]
    Correct Answer :-
    • 0 [Option ID - 17168]
30. 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]

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    2. Principal component analysis [Option ID - 17171]
    3. Factor analysis [Option ID - 17172]
    4. None of these [Option ID - 17173]
    Correct Answer :-
    • Discriminant analysis [Option ID - 17170]

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31. If Y ~ N(µ, S) with µ = $\left(\begin{array}{ccc}2& 3& 1\end{array}\right)$ and S = $\left(\begin{array}{ccc}3& -1& 2\\ -1& 2& 1\\ 2& 1& 5\end{array}\right)$ then the joint distribution of y1, y2, and (y2 + y3) is
32. 1. N3 $(\begin{array}{ccc}2& 3& 4\end{array},\begin{array}{ccc}3& -1& 2\\ -1& 2& 1\\ 2& 1& 5\end{array})$ [Option ID - 17174]
    2. N3 $\left(\begin{array}{ccc}3& -2& 2.0\\ -2& 2& 1.0\\ 0.5& 2.0& 1.5\end{array}\right)$ [Option ID - 17175]
    3. N3 $\left(\begin{array}{ccc}3& -2& 2.0\\ -2& 2& 1.0\\ 0.5& 2& 1.5\end{array}\right)$ [Option ID - 17176]
    4. None of these [Option ID - 17177]

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    Correct Answer :-
    • N3 $\left(\begin{array}{ccc}3& -2& 2.0\\ -2& 2& 1.0\\ 0.5& 2& 1.5\end{array}\right)$ [Option ID - 17176]
33. Let X1, X2, ...., X? be a random sample from a distribution with finite mean µ. Consider an estimator T = (1/n)?X?² for estimating µ². Which of the following statement is true? [Question ID = 4296]
    1. T is unbiased and consistent [Option ID - 17178]
    2. T is neither unbiased nor consistent [Option ID - 17179]
    3. T is biased but consistent [Option ID - 17180]

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    4. T is unbiased but not consistent [Option ID - 17181]
    Correct Answer:-
    • T is biased but consistent [Option ID - 17180]
34. Let X1, X2, ......., X? be a random sample from U(-?,?) distribution. Maximum likelihood estimator of ? is [Question ID = 4297]
    1. X(?), the nth order statistic [Option ID - 17182]
    2. X¯ [Option ID - 17183]

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    3. X(1), the first order statistic [Option ID - 17184]
    4. -X(1) [Option ID - 17185]
    Correct Answer :-
    • -X(1) [Option ID - 17185]
35. Let X1, X2, ..., X? be i.i.d N(µ, s²), both µ and s² unknown. Which of the following is a minimal sufficient statistic for (µ, s²)? [Question ID = 4298]
    1. (X¯, s²), where s² = (1/(n-1))?(X? - X¯)² www.FirstRanker.com

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    2. (?X?, ?X?²) [Option ID - 17187]
    3. (?X?, ?(X? - X¯)²) [Option ID - 17188]
    4. All of these [Option ID - 17189]
    Correct Answer :-
    • All of these [Option ID - 17189]

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36. Which of the following tests can be considered as a non-parametric equivalent of one-way repeated measures ANOVA? [Question ID = 4299]
    1. Kruskal-Wallis test [Option ID - 17190]
    2. Mann-Whitney U test [Option ID - 17191]
    3. Friedman test [Option ID - 17192]
    4. Kolmogorov-Smirnov test [Option ID - 17193]
    Correct Answer :-
    • Friedman test [Option ID - 17192]

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37. Consider a random sample of size 3 from an exponential distribution with mean ?. Let the critical region for testing H0: ? = 2 against H1: ? = 1 be defined as, W = {X: X1 + X2 + X3 = 9.5}. Then, the size of the critical region and the power of the test will be, respectively? [Question ID = 4300]
    1. P[Y = 9.5], P[Y = 19]; where Y~?²(6) [Option ID - 17194]
    2. P[Y = 9.5], P[Y = 19]; where Y~?²(3) [Option ID - 1
       

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