If a random variable X follows binomial distribution with mean 5 and variance $\frac{5}{2}$, then $P(X \leq 9)$ is :

If $X$ is a Poisson variate such that $4P(X=1)=3P(X=2)$, then $P(X=0)=$

A discrete random variable X has the following probability distribution :

The value of b is :

Which of the following statements are correct ?

(A) $\text{var}(aX + b) = a^2 \text{var}(X)$

(B) $\text{var}(X) = E(X^2) - \{E(X)\}^2$

(C) $E(aX + b) = aE(X) + b$

(D) $E(X) = \sum_{i=1}^{n} p_i x_i^2$

Choose the correct answer from the options given below :

If the heights of 300 students are normally distributed with mean 68 inches and standard deviation 3 inches. If Z is the standard normal variate such that $P(0\le Z\le 1.33)=0.4082, P(Z\ge 1.33)=0.0918$ and $P(0\le Z\le 1)=0.3413$, then which of the following statements are correct?

(A) There are 27 students whose height is greater than 72 inches.

(B) The number of students having heights less than or equal to 64 inches is 27.

(C) 210 students have their heights between 65 and 71 inches.

(D) There are 35 students whose height is greater then 72 inches.

Choose the correct answer from the options given below:

For 6 trials of an experiment, let X be a binomial variate which satisfies the relation $9P(X=4)=P(X=2)$, then the probability of success is

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