1.
If is a probability density function then the value of k is
(1) (2) (3) (4)
A. 
B. 
C. 
D. 
2.
If is a p.d.f of a continuous random variable X, then the value of A is
(1) 16 (2) 8 (3) 4 (4) 1
A. 
B. 
C. 
D. 
3.
A random variable X has the following probability distribution
X
0
1
2
3
4
5
P(X=x)
1/4
2a
3a
4a
5a
1/4
Then is
(1) (2) (3) (4)
A. 
B. 
C. 
D. 
4.
A random variable X has the following probability mass function as follows:
X
-2
3
1
P(X=x)
Then the value of is
(1) 1 (2) 2 (3) 3 (4) 4
A. 
B. 
C. 
D. 
5.
A random variable X has the following p.d.f.
X
0
1
2
3
4
5
6
7
P(X=x)
0
Then the value of is
(1) (2) (3) 0 (4) or
A. 
B. 
C. 
D. 
6.
X is a discrete random variable which takes the value 0, 1, 2 and , then the value of is
(1) (2) (3) (4)
A. 
B. 
C. 
D. 
7.
Given and then the value of is
(1) - 2 (2) 4 (3) - 4 (4) 2
A. 
B. 
C. 
D. 
8.
is
(1) 7 (2) 16Var(X) (3) 19 (4) 0
A. 
B. 
C. 
D. 
9.
X is a random variable taking the values 3 , 4 and 12 with probabilities and . Then is
(1) 5 (2) 7 (3) 6 (4) 3
A. 
B. 
C. 
D. 
10.
Variance of the random variable X is 4. Its mean is 12. then is
(1) 2 (2) 4 (3) 6 (4) 8
A. 
B. 
C. 
D. 
11.
The mean of a binomial distribution is 5 and its standard deviation is 2. Then the value of n and p are
(1) (2) (3) (4)
A. 
B. 
C. 
D. 
12.
For a discrete random variable X. Then the mean of the random variable X is
(1) 16 (2) 5 (3) 2 (4) 1
A. 
B. 
C. 
D. 
13.
If the mean and standard deviation of a binomial distribution are 12 and 2 respectively. Then the value of its parameter p is
(1) (2) (3) (4)
A. 
B. 
C. 
D. 
14.
In 16 throws of a die getting an even number is considered a success. Then the variance of the successes is
(1) 4 (2) 6 (3) 2 (4) 256
A. 
B. 
C. 
D. 
15.
In 5 throws of a die, getting 1 or 2 is a success. The mean number of successes is
(1) (2) (3) (4)
A. 
B. 
C. 
D. 
16.
If two cards are drawn from a well shuffled pack of 52 cards, the probability that they are of the same colours is
(1) (2) (3) (4)
A. 
B. 
C. 
D. 
17.
If in a poisson distribution then the variance is
(1) (2) (3) (4)
A. 
B. 
C. 
D. 
18.
If a random variable X follows Poisson distribution such that then the variance of the distribution is
(1) 6 (2) 5 (3) 30 (4) 25
A. 
B. 
C. 
D. 
19.
A box contains 6 red and 4 white balls. If 3 balls are drawn at random, the probability of getting 2 white balls is
(1) (2) (3) (4)
A. 
B. 
C. 
D. 
20.
The distribution function F(X) of a random variable X is
(1) a decreasing function (2) an increasing function (3) a constant function (4) increasing first and then decreasing
A. 
B. 
C. 
D. 
21.
For a Poisson distribution with parameter the value of the moment about the origin is
(1) 0.25 (2) 0.3125 (3) 0.0625 (4) 0.025
A. 
B. 
C. 
D. 
22.
In a Poisson distribution if then the value of its parameter is
(1) 6 (2) 2 (3) 3 (4) 0
A. 
B. 
C. 
D. 
23.
If f(x) is a p.d.f of a normal distribution with mean then is
(1) 1 (2) 0.5 (3) 0 (4) 0.25
A. 
B. 
C. 
D. 
24.
The random variable X follows normal distribution then the value of is
(1) (2) (3) (4)
A. 
B. 
C. 
D. 
25.
If f(x) is a p.d.f. of a normal variate and then is
(1) undefined (2) 1 (3) .5 (4) -.5
A. 
B. 
C. 
D.