If \(f\left( x \right) =\begin{cases} k{ x }^{ 2 },0 is a probability density function then the value of k is.
A1/3
B1/6
C1/9
D1/12
Question - 2
If \(f\left( x \right) =\frac { A }{ \pi } \frac { 1 }{ 16+{ x }^{ 2 } } ,-\infty is a p.d.f of a continuous random variable X, then the value of A is.
A16
B8
C4
D1
Question - 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 \(P\left( 1\le x\le 4 \right) \) is...
A10/21
B2/7
C1/14
D1/2
Question - 4
X is a discrete random variable which takes the values 0,1,2 and P(X =0) = 144 / 169, P(X=1) = 1/169 then the value of P(X=2) is.
A145/169
B24/169
C2/169
D143/169
Question - 5
Given E(X +c) = 8 and E (X –c) = 12 then the value of c is.
A-2
B4
C-4
D2
Question - 6
X is a random variable taking the values 3,4 and 12 with probabilities 1/3, 1/4 and 5 / 12 . Then E(X) is.
A5
B6
C7
D3
Question - 7
Variance of the random variable X is 4. Its mean is 2 . Then E(X²) is
A2
B4
C6
D8
Question - 8
In 5 throws of a die, getting 1 or 2 is a success. The mean number of successes is
A5/3
B3/5
C5/9
D9/5
Question - 9
The mean of binomial distribution is 5 and its standard deviation is 2. Then the value of n and p are.
A\(\left( \frac { 4 }{ 5 } ,25 \right) \)
B\(\left( 25,\frac { 4 }{ 5 } \right) \)
C\(\left( \frac { 1 }{ 5 } ,25 \right) \)
D\(\left( 25,\frac { 1 }{ 5 } \right) \)
Question - 10
If the mean and standard deviation of a binomial distribution are 12 and 2 respectively. Then the value of its parameter p is.