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
`quad p(x) = {((6)/(pi^2 x^2) for x=1 ; -2 ; 3 ; -4 ...),(0 elsewhere):}`
Then
Answer
D. `quadE(X)<oo` , but `quadE(X)` does not exist
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)=`
`quadf(x,y)={(1/8(6-x-y) 0<=x<2; 2<=y<4),(0 "elsewhere"):}`
Then `quadP(X+Y<3)=`
Answer
A. `5/24`
53
If `quadX` and `quadY` are two random variables having finite expectations, then the value of `quadE["min"{X,Y}+"max"{X,Y}]` is
Answer
D. equal to`quadE(X+Y)`
54
The Poisson distribution `quadP(Lambda)` is unimodal when
Answer
A. `quadlambda` is not an integer
55
Which of the following distribution is not a member of power series family of distributions?
Answer
D. Hypergeometric
56
If `quadX` follows normal `quadN(mu,sigma)` , then the approximate value of `quadE{|X-mu|}` is
Answer
C. `quad4/5sigma`
57
If `quadX` is uniformly distributed with mean unity and variance 0.75, then `quadP(X>1)=`
Answer
B. 0.5
58
If `quadX` follows normal `quadN(mu,Sigma)` , then `quadY=e^X` follows
Answer
A. Log-normal distribution
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}`
Answer
C. `quadE(sum_(j=1)^nTheta_j)`
60
The mode of `quadF` -distribution is
Answer
A. always less than unity
61
"Simple random sampling" is the technique of drawing a sample in such a way that each unit of the population has
Answer
D. an equal and independent chance of being included in the sample
62
In SRSWR with usual notations, the standard error of the sample mean `quadbary` is
Answer
B. `quadS({N-1}/{Nn})^{1/2}`
63
The formulae for optimum allocation in various strata in stratified sampling were first derived by
Answer
A. Tschuprov
64
The ratio estimator of population mean is unbiased if sampling is done according to
Answer
A. PPSWR
65
The cluster sampling is more efficient when
Answer
C. both (A) and (B)
66
Local control is a device to maintain
Answer
A. homogeneity within blocks
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?
(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?
Answer
B. (i) and (iii) are linear contrasts
68
While analyzing the data of a `quadkxxk` Latin Square Design, the degrees of freedom in the ANOVA is
Answer
D. `quad(k-1)(k-2)`
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
Answer
B. 12
70
If the interactions `quadAB` and `quadBC` are confounded with incomplete blocks in a `quad2^n` factorial experiment, then automatically confounded effect is
Answer
C. `quadAC`
71
Which among the following is a consistent estimator of the population mean when samples are from the Cauchy population?
Answer
B. Sample median
72
If the regularity conditions of the CR inequality are violated then the least attainable variance will be
Answer
C. less than the CR bound
73
A method to obtain the UMVUE is by using
Answer
D. Lehmann-Scheffe Theorem
74
A complete-sufficient statistic for `p` in the Bernoulli distribution
`(x, p) = p^x (1-p)^x; x=0, 1.
= 0 `"otherwise"` is
`(x, p) = p^x (1-p)^x; x=0, 1.
= 0 `"otherwise"` is
Answer
C. `sum_(i=1)^n X_i`
75
The least square estimators are
Answer
D. All these
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