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

X	30	10	-10
P(X)	1/5	3/10	1/2

then E(X) is equals to

If the mean of a binomial distribution is 12 and its standard deviation is 2, then the number of trials is :

In binomial distribution with $n = 10$ and $P = \frac{1}{3}$, the probability of the event that unequal number of failures and successes occur is :

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 $e^{-2} =0.1353$]

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 $X$ is a Poisson variate such that $P(X=3)=2P(X=4)$, then $P(X=2)$ equals:

[given $e^{-2}=0.14$]

A discrete random variable X takes the values 0, 1, 2, 3, 4 and its mean is 1.6. If $P(X=1) = 0.4$, $P(X=4) = P(X=2)$ and $P(X=3) = 2P(X=2)$, then $P(X=0)$ is :