If $f(x) = \frac{x+2}{18}$ for $-2 < x < 4$ and $f(x) = 0$ otherwise,is the probability density function (p.d.f.) of a random variable $X$,then the value of $P(|X| < 2)$ is

Let $X$ be a random variable such that the probability function of a distribution is given by $P(X=0) = \frac{1}{2}$ and $P(X=j) = \frac{1}{3^j}$ for $j = 1, 2, 3, \ldots, \infty$. Then the mean of the distribution and $P(X \text{ is positive and even})$ respectively are:

If the function $P[X = x] = \begin{cases} \frac{K \cdot 2^x}{x!}, & x = 0, 1, 2, 3 \\ 0, & \text{otherwise} \end{cases}$ forms a probability mass function (p.m.f.),then the value of $K$ is:

If $X$ is a Poisson variate with $P(X=0)=0.8$,then the variance of $X$ is

Let $X$ be a discrete random variable. The probability distribution of $X$ is given below:

$X$	$30$	$10$	$-10$
$P(X)$	$\frac{1}{5}$	$A$	$B$

If $E(X) = 4$,then the value of $AB$ is equal to:

Find the variance of the number obtained on a throw of a fair die.