The probability distribution of a discrete random variable is given below :

X	1	2	3	4	5
P(X)	1/5	m	2/5	2m	3m

Which of the following are correct?

A. $P(2)=\frac{1}{15}$

B. $P(4)=\frac{2}{15}$

C. $P(X<2)=\frac{1}{5}$

D. $P(X\geq4)=\frac{1}{5}$

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.

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There are 10% defective pens. In a sample of randomly selected 10 pens, the probability that atmost one pen is defective, is

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

A random variable X follows Poisson distribution. The variance of X is 2. The value of $P(X=3)$ is

The probability distribution of a random variable X is given below :

Then, $\text{Var}\left(\frac{X}{2}\right)$ is :

If X is a random variable which can take values 0,1,2,3 such that $E(X^2) = 2E(X)$.

If $P(X=0) = P(X=1) = m\ \&\ P(X=2) = 2m$, then which of the following are TRUE?

A. $P(X=1) = \dfrac{1}{13}$

B. $P(X=3) = \dfrac{1}{13}$

C. $E(X) = \dfrac{18}{13}$

D. $P(X=2) = \dfrac{6}{13}$

Choose the correct answer from the options given below: