Let $X$ be a discrete random variable whose probability distribution is defined as follows;

$P(X=x)=\begin{cases}k(x+1), & x=1,2,3,4\\ 2kx, & x=5,6,7\\ 0, & \text{otherwise}\end{cases}$

where $k$ is constant, then $P(X=5)$ is equal to

A random variable X has the following probability distribution:

Which of the following are correct?

(A) $P(X \le 1)=0.25$

(B) $P(X>3)=0.15$

(C) $P(X=2)=0.30$

(D) $P(X \le 2)=0.55$

Choose the correct answer from the options given below:

Which of the following statements are correct?

(A) The mean of a binomial distribution is always greater than the variance.

(B) The mean of a Poisson distribution is always greater than the variance.

(C) If $f(x)$ is the probability density function of a random variable $X$, then $P(a \leq X \leq b) = \int_a^b f(x)dx$.

(D) If $X$ is a random variable and $a,b$ are real numbers, then $Var(aX+b)=a^2Var(X)$.

Choose the correct answer from the options given below:

If the probability distribution of X is :

Then variance is equal to :

Match List - I with List - II.

Choose the correct answer from the options given below :

In a binomial distribution the probability of getting success is $\frac{1}{4}$ And standard deviation is 3 then its mean is ?

If X has a Poisson distribution such that $P(X = 1) = P(X = 2)$ then $P(X = 3)$ is :