D2 = ((N_1.N_2))/((N_1+N_2)) T*2°
D*2 =((N_1 N_2))/((N_1-N_2)) T*2°
D*2 = ((N_1-N_2))/((N_1 N_2)) T*2°
D*2 = ((N_1 + N_2))/((N_1 N_2)) T*2
Correct Answer:- Option-D

Question89:-In principal component analysis the variances of the Principal Components are the of the covariance
matrix.

A:-diagonal elements
B:-eigen values
C:-normalized elements
D:-non-zero elements
Correct Answer:- Option-B

Question90:-For discriminating between two populations R.A. Fisher suggested the linear discriminant function *X'l’ for
which

റയ

A:~ ("(mean difference)"*2)/("variance")*
B:-\("mean difference")*2/("A.M.")°
C:-\("mean difference")/("median")*

:-*("variance")/("mean difference")*

Correct Answer:- Option-A
Question91:-Assume that the time to failure ‘(T) for a certain bulb has an exponential distribution “f ((t)/(lambda)) with
Parameter ‘lambda >0° with the prior pdf *g (lambda)* of ‘lambda’ is an exponential distribution with parameter 2. Then
the posterior pdf of ‘lambda* given ‘T = ലട

(2/2)
*(lambda)/(e*lambda (t+2))°
(lambda e*(lambda (t+2)))/((t+2)*2)°
+" (lambda (t+2)*2)(e* (lambda (t+2)))*

Correct Answer:- Option-D
Question92:-The basic elements of statistical decision theory is

A:-a space Q ‘= {ul theta} of all possible states of nature

B:-an action space ‘A = {a}* of all possible courses of action

C:-a loss function ‘L (ul theta, a)’ giving the incurred loss when action ‘a* is taken and the state is * ul theta*

D:-all these

Correct Answer:- Option-D
Question93:-When there is no censoring for the life length *T*, the general formula of a survival function is

A:-‘hat {S (t)} = (" # of individuals with" T >= t)/("total sample size")

B:-hat {S (t)} = (" # of individuals with" T <= t)/("total sample size")*

(:-॥ {S (t)} = (" # of individuals with" T = t)/("total sample size")*

D:-hat {S (t)} = (" # of individuals with" T = 0)/("total sample 5126")

Correct Answer:- Option-A
Question94:-The Cox's Proportional Hazard Model (Cox's PH Model) with explanatory variables * ul X = (X_1, X_2, ... X_p),
beta_i’ their regression coefficients and ‘h_0 (t)’ a base line hazard, is *h (t, ul X) ="
A:-‘e* {h_0 (t) sum_(i=1)*p beta_i X_i}*
log h_O (t) + sum_(i=1)*p beta_i X_i*
C:-h_O (t) e sum_(i=1)*p beta_i X_i
D:-*e*(h_0 (t)) sum_(i=1)*p beta_i X_°

Correct Answer:- Option-C
Question95:-When an inspection lot contains no defectives the OC function ` । (p)* is

8: | (0) = 00`
0:- 1 (9) =
D:-None of these
Correct Answer:- Option-A
Question96:-In a Time series data, the two main components which cause lack of stationarity are
A:-Seasonal and irregular variations
B:-Cyclic and irregular variations
C:-Trend and cyclic variations
D:-Trend and seasonal variations
Correct Answer:- Option-D

Question97:-In the ARMA (1, 1) model *Z_t = ‘phi Z_{t-1} + epsilon t - theta epsilon_{t-1}° the condition for stationarity
and invertilibility are respectively