Match the LIST-I with LIST-II

	LIST-I		LIST-II
A.	In a binomial distribution, if $n = 16$, $p = 0.75$, then the mean is	I.	$4$
B.	In a binomial distribution, if $n = 25$, $p = \dfrac{1}{5}$, then variance is	II.	$32$
C.	In a binomial distribution, the mean is 8 and the variance is 6, then the number of trials is	III.	$18$
D.	If the mean and variance of a binomial distribution are 6 and 4 respectively, then the number of trials is	IV.	$12$

Choose the correct answer from the options given below:

The probability distribution of a discrete random variable X is given by :

then E(X) is equals to

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 mean of a binomial distribution is 24 and its standard deviation is 4 , then the probability of getting success is :

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

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

Where $k$ is an arbitrary constant, then $E(X)$ is equal to:

Let X denote the number of scores in a test. If X is normally distributed with mean 100 and standard deviation 15, then the probability that X does not exceed 130 is,

(Given $P(0 \le Z \le 2)=0.4772$, where $Z$ be the standard normal variate)

If 0.1% of the bolts manufactured by a machine are found to be defective. Find the probability that, in a sample of 2000 bolts chosen at random, exactly 3 will be defective using the Poisson distribution. [Given $e^{-2} =0.1353$]