Correct Answer:- Option-D
Question32:-For the sequence of random variables *{X_(n)}* such that *P[X_(n)=+-2%(n)]=(1)/(2),n=1, 2, ...°
A:-WLLN holds
B:-WLLN does not hold
C:-SLLN holds
D:-None of these
Correct Answer:- Option-B
Question33:-Let X be a random variable having t-distribution with n degrees of freedom. Then the distribution of
1/2) 6
A:-F distribution with (n, 1) degrees of freedom
B:-F distribution with (1, n) degrees of freedom
C:-chi*(2)* distribution with n degrees of freedom
D:-‘chi*(2)° distribution with n — 1 degrees of freedom
Correct Answer:- Option-A
Question34:-The joint density function of *X_(1)° and *X_(2)* is
f(x_(1),x_(2))=e*(-(x_(1)+x_(2)), *x_(1)>0, x_(2)>0)
The distribution of *(X_(1))/(X_(1)+X_(2))* will be
A:-Gamma distribution with parameters 1 and 2
B:-Exponential with parameter 2
C:-Uniform in the interval (0, 1)
D:-None of these
Correct Answer:- Option-C
Question35:-The mode of F-distribution with *(n_(1),n_(2))* degrees of freedom is

)2 - 71012
)2 + 7( مر
)2 - 111( 112

8.11 012 + 2)
N, (Nz + 2)
ಯ್‌ 71, (01, 7 2)
72 (701 + 2)

p. 704 (702 )
Correct Answer:- Option-B
Question36:-The joint probability distribution of two random variables X and Y are given by:

P{X=—1, Y=0}=P{X=0, Y=0}=P{X=0, Y=1} = P{X=1, Y=0}="(1)/(8)° and P{X=-1, Y= X=1, Y=-1}="(1)/(4)°.
Obtain the conditional probability distribution of X given Y = 1.
0 | -1 ] ٤اا‎ 1
f(x/y=1) 2 2 | ¢ |
Kes 6 3
% -1 | 0 | 1
f(x/y=1) 3 1 ட்‌
3 3 3
B:-
0 | -1 | 0 | 3
f(x/y=1) 2 1 | ० |
ಯ. ತಿ ತಿ
೫ -1 | 0 |
5 f(x/y=1) 1 | 0 | | 0 |