PSC HSST Statistics Model Questions and Answers

51. Let `quadX` be a random variable with probability mass function
`quad p(x) = {((6)/(pi^2 x^2) for x=1 ; -2 ; 3 ; -4 …),(0 elsewhere):}`
Then
(A) `quadE(X)=oo`
(B) `quadE(X)` exists
(C) `quadE(X)<oo` and `quadE(X)` exists
(D) `quadE(X)<oo` , but `quadE(X)` does not exist
Answer: D

52. Let `quad(X,Y)` has joint density
`quadf(x,y)={(1/8(6-x-y) 0<=x<2; 2<=y<4),(0 “elsewhere”):}`
Then `quadP(X+Y<3)=`
(A) `5/24`
(B) `5/8`
(C) `3/8`
(D) None of these
Answer: A

53. If `quadX` and `quadY` are two random variables having finite expectations, then the value of `quadE[“min”{X,Y}+”max”{X,Y}]` is
(A) less than `quadE(XY)`
(B) less than `quadE(X+Y)`
(C) equal to `quadE(XY)`
(D) equal to`quadE(X+Y)`
Answer: D

54. The Poisson distribution `quadP(Lambda)` is unimodal when
(A) `quadlambda` is not an integer
(B) `quadlambda` is an integer
(C) Both (1) and (2)
(D) Neither (1) nor (2)
Answer: A

55. Which of the following distribution is not a member of power series family of distributions?
(A) Binomial
(B) Poisson
(C) Geometric
(D) Hypergeometric
Answer: D

56. If `quadX` follows normal `quadN(mu,sigma)` , then the approximate value of `quadE{|X-mu|}` is
(A) Zero
(B) `sigma`
(C) `quad4/5sigma`
(D) `quadsqrt(4/Pi)sigma`
Answer: C

57. If `quadX` is uniformly distributed with mean unity and variance 0.75, then `quadP(X>1)=`
(A) 0.25
(B) 0.5
(C) 0.75
(D) 1
Answer: B

58. If `quadX` follows normal `quadN(mu,Sigma)` , then `quadY=e^X` follows
(A) Log-normal distribution
(B) Exponential distribution
(C) Logistic distribution
(D) Pareto distribution
Answer: A

59. If `quadX_j` follows exponential `quadE(Theta_j)` distribution, for `quadj=1,2,…,n,` then the distribution of `quad”min”{X_1,X_2,…,X_n}`
(A) `quadE(Theta_j)`
(B) ` E (prod_{j=1}^n theta_j)`
(C) `quadE(sum_(j=1)^nTheta_j)`
(D) `quadE[“min”{Theta_1,Theta_2,…,Theta_n}]`
Answer: C

60. The mode of `quadF` -distribution is
(A) always less than unity
(B) sometimes less than unity
(C) always greater than unity
(D) sometimes equal to unity
Answer: A

61. “Simple random sampling” is the technique of drawing a sample in such a way that each unit of the population has
(A) distinct and dependent chance of being included in the sample
(B) distinct but independent chance of being included in the sample
(C) an equal but dependent chance of being included in the sample
(D) an equal and independent chance of being included in the sample
Answer: D

62. In SRSWR with usual notations, the standard error of the sample mean `quadbary` is
(A) `quadS({N-n}/{Nn})^{1/2}`
(B) `quadS({N-1}/{Nn})^{1/2}`
(C) `quadS(1-{n}/{N})^{1/2}`
(D) `quadS/n(1-{1}/{N})^{1/2}`
Answer: B

63. The formulae for optimum allocation in various strata in stratified sampling were first derived by
(A) Tschuprov
(B) Cochran
(C) Lahiri
(D) Neymann
Answer: A

64. The ratio estimator of population mean is unbiased if sampling is done according to
(A) PPSWR
(B) PPSWOR
(C) SRSWR
(D) SRSWOR
Answer: A

65. The cluster sampling is more efficient when
(A) the variation within clusters in more
(B) the variation between clusters is less
(C) both (A) and (B)
(D) neither (A) nor (B)
Answer: C

66. Local control is a device to maintain
(A) homogeneity within blocks
(B) homogeneity among blocks
(C) both (A) and (B)
(D) neither (A) nor (B)
Answer: A

67. In a linear model `quadY_{ij}=alpha_i+e_{ij},` `quadj=1,2,…,n_i;` `quadi=1,2,…,k,` consider
(i) `quadalpha_1-3alpha_2+alpha_3+alpha_4`
(ii) `quadalpha_1+3alpha_2-alpha_3-alpha_4`
(iii) `quadalpha_1+3alpha_2-2alpha_3-2alpha_4`
Then which of the following is correct?
(A) (i) and (ii) are linear contrasts
(B) (i) and (iii) are linear contrasts
(C) (ii) and (iii) are linear contrasts
(D) (i), (ii) and (iii) are linear contrasts
Answer: B

68. While analyzing the data of a `quadkxxk` Latin Square Design, the degrees of freedom in the ANOVA is
(A) `quadk^2-1`
(B) `quadk-1`
(C) `quadk^2-2k+1`
(D) `quad(k-1)(k-2)`
Answer: D

69. In a split plot design with factor `quadA` at 3 levels in main plots, factor `quadB` at 3 levels in sub-plots and 3 replications, the degrees of freedom for sub-plot error is
(A) 27
(B) 12
(C) 8
(D) 4
Answer: B

70. If the interactions `quadAB` and `quadBC` are confounded with incomplete blocks in a `quad2^n` factorial experiment, then automatically confounded effect is
(A) `quadA`
(B) `quadC`
(C) `quadAC`
(D) `quadABC`
Answer: C

71. Which among the following is a consistent estimator of the population mean when samples are from the Cauchy population?
(A) Sample mean
(B) Sample median
(C) Sample variance
(D) None of these
Answer: B

72. If the regularity conditions of the CR inequality are violated then the least attainable variance will be
(A) equal to the CR bound
(B) greater than the CR bound
(C) less than the CR bound
(D) zero
Answer: C

73. A method to obtain the UMVUE is by using
(A) Rao-Blackwell Theorem
(B) Baye’s Theorem
(C) Neymann-Pearson Theorem
(D) Lehmann-Scheffe Theorem
Answer: D

74. A complete-sufficient statistic for `p` in the Bernoulli distribution
`(x, p) = p^x (1-p)^x; x=0, 1.
= 0 `”otherwise”` is
(A) The first order statistic `X_{(1)}`
(B) The `n` `”^{th}”` order statistic `X_{(n)}`
(C) `sum_(i=1)^n X_i`
(D) `X_{(n)}-X_{(1)}`
Answer: C

75. The least square estimators are
(A) Unbiased
(B) BLUE
(C) UMVUE
(D) All these
Answer: D