Correct Answer:- Option-C

Question37:-If X~B (n, 0.5), n being an odd number, the binomial distribution has a maximum probability at the
value/values

८० (1-1)/(2):
(n+1)/(2)
(n-1)/(2) and(n+1)/(2)*

D:-*(n)/(2)-1° and *(n)/(2)+1°

Correct Answer:- Option-C
Question38:-If X follows power series distribution with probability density function *P{X=x}=(a_(x)theta~(x))/(f(theta)), x=1,
2, ...; 2>0` and zero elsewhere, where “f(theta) * ="sumquad_(xepsiS)* ‘a _(x)theta%(x)* is a generating function; S is a
nonempty countable set of non-negative integers, then for what values of @ and f(@) does this distribution follows negative
binomial distribution.

A:- theta=(p)/(1-p),f(theta)=(1+theta)*(n)*
8:- theta=(p)/(1+p),f(theta)=(1-theta)*(-n)*
C:- theta=(p)/(1-p),f(theta)=(1-theta) *(n)*
D:-theta=(p)/(1+p),f(theta)=(1+theta)“(-n)*
Correct Answer:- Option-B

Question39:-If X and Y are independent Gamma variates with parameters 5 and 8, then *(X)/(Y)° follows distribution.
A: beta_(1)* (8, 5)
B:- beta_(1)* (5, 8)
C:-‘beta_(2)° (8, 5)
D:-beta_(2)° (5, 8)
Correct Answer:- Option-D

Question40:-Let *X_(1)°, (2), ... ന)”, ൧൦ ന independent and identically distributed random variables with p.d.f. f(x)
and c.d.f. F(x), then the cumulative distribution function of the smallest order statistic is

[F(x)]*(n)°
[1-F(x)]*(n)°
120001൫൪
-[1-F(x)]*(n)°

ഉ:
Correct Answer:- Option-D
Question41:-Mode and Karl Pearson's coefficient of skewness of a ‘chi*(2)* distribution, with n degrees of freedom, are at

A:-x =n — 2 and ‘sqrt((2)/(n))*
n—2 and ‘sqrt((1)/(n))*
6 nand ` 501((2)/(1))`
D:-x = n and “sqrt((1)/(n))*
Correct Answer:- Option-A

Question42:-The median of F distribution when *n_(1)° = ‘n_(2)* is at and the quartiles *Q_(1)° and ‘Q_(3)° satisfy
the condition
=0, 0_(1)0_(3)-1'
, 0 (1)0 (3)=1`
5, 0 (1)0 (3)=1`

0:- 0.75, 0 (110 (3)=1

Correct Answer:- Option-B
Question43:-If *phi*(x, y, p) denote the density function of *N_(2)(0, sum)* , where *sum=[[1,rho],[rho,1]]° then which of the
following is true for *Psi(x, y)=(1)/(2)[phi(x, y, 0.5)+phi(x, ५, -0.5] ?

A:- Psi’ (x, y) is bivariate normal

B:-X and Y are independent

C:-X and Y are following N(0, 1)

D:-None of the above

Correct Answer:- Option-C
Question44:-In a trivariate distribution *X_(1),X_(2)° and *X_(3)*, given that ‘r_(12)=0.7", ‘r_(23)=r_(13)=0.5° . Then the
partial correlation between *X_(2)* and *X_(3)° is

A:-0.342

67

D:-0
Correct Answer:- Option-B

Question45:-If all the simple correlation coefficients in a set of p-variables are equal to ‘rho’, then every first order partial
correlation coefficients are

4:- ` 1-10^(2)`