Kerala PSC Previous Years Question Paper & Answer

Title : HSST - STATISTICS - SPECIAL RECRUITMENT FOR SC / ST AND ST ONLY
Question Code : A

Page:6


Below are the scanned copy of Kerala Public Service Commission (KPSC) Question Paper with answer keys of Exam Name 'HSST - STATISTICS - SPECIAL RECRUITMENT FOR SC / ST AND ST ONLY' And exam conducted in the year 2017. And Question paper code was '016/2017/OL'. Medium of question paper was in Malayalam or English . Booklet Alphacode was 'A'. Answer keys are given at the bottom, but we suggest you to try answering the questions yourself and compare the key along wih to check your performance. Because we would like you to do and practice by yourself.

page: 6 out of 12
Excerpt of Question Code: 016/2017/OL

Question45:-If *quadx* is a random variable with finite expectation, then the value of *quadxP(X<-x)* as ‘quadx->00° is
A:-infinity
B:-unity
C:-zero
D:-indeterminate
Correct Answer:- Option-C
Question46:-If *quadx* is a symmetric random variable with distribution function ‘quadF* and real valued characteristic

function ©, then for any ‘quadx* in R , quadF(x)="
A:- quadF(-x)*
8:- quadF(-x-0)°
C:-*quadF(-x-0)-1"
D:- quad 1-F(-x-0)*
Correct Answer:- Option-D

R

Question47:-If the characteristic function © of distribution function ‘quadF* is absolutely integrable on ~", then for
SR
any’ quadx* in ೫ , quad f'={dF(x)}/dx" is
A:-bounded

B:-uniformly continuous

C:-both (1) and (2)

D:-Neither (1) nor (2)

Correct Answer:- Option-C
Question48:-Let ‘quadX* and ‘quadX_n* be independent standard normal variables on a probability space (Q, quadfrA,P)* *
*, for *quadn>=1* . Then which of the following is not true?

A:-X_nstackrel(P)(->)X*

B:-X_nstackrel(d)(->)X*

C:-quadE(X_n-X)=0°

D:- quadVar(X_n-X)=2°

Correct Answer:- Option-A
Question49:-The sequence *quad{X_n}° of independent random variables, each with finite second moment, obeys SLLN if

A:-quadsum_(k=1)“ooVar(X_k)
B:-quadsum_(k=1)“oo{Var(X_k)}/k
C:-‘quadsum_(k=1)*00{Var(X_k)}/sqrt(k)<0o*

D:- quadsum_(k=1)*o0{Var(X_k)}/k*2
Correct Answer:- Option-D
Question50:-Let ‘quad {X_n}* sequence of independent random variables with
*quadP(X_k=+-k)=1/2k*-Lambda* and ‘quadP(X_k=0)=1-k*-Lambda® , for ‘quadk>=1*
Then the sequence does not obey CLT if

A:-quadLambda=0"

B:-‘quadLambda=1*

C:-quadLambdain(0,1/2)*

0:- quadLambdain(1/2,1)*

Correct Answer:- Option-B
Question51:-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)=00°
B:-‘quadE(X)* exists
C:-‘quadE(X)D:- quadE(X)
Correct Answer:- Option-D
Question52:-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)="

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