$A$ box contains $10$ pens of which $3$ are defective. $A$ sample of $2$ pens is drawn at random and let $X$ denote the number of defective pens. Then the variance of $X$ is

The cumulative distribution function (c.d.f.) $F(x)$ of a discrete random variable $X$ is given by the following table:

$X$	$-3$	$-1$	$0$	$1$	$3$	$5$	$7$	$9$
$F(X=x)$	$0.1$	$0.3$	$0.5$	$0.65$	$0.75$	$0.85$	$0.90$	$1$

Then,find the value of $\frac{P[X=-3]}{P[X < 0]}$.

$A$ bag contains $2$ white and $1$ red balls. One ball is drawn at random and then put back in the box after noting its colour. The process is repeated again. If $X$ denotes the number of red balls recorded in the two draws,describe $X$.

If $m$ and $\sigma^2$ are the mean and variance of the random variable $X$,whose distribution is given by:

$X=x$	$0$	$1$	$2$	$3$
$P(X=x)$	$\frac{1}{3}$	$\frac{1}{2}$	$0$	$\frac{1}{6}$

Then:

$A$ $1$-rupee coin,a $2$-rupee coin,a $5$-rupee coin,and a $10$-rupee coin are tossed simultaneously. The expected value of the sum of the values of the coins that show heads up is:

Two balls are drawn at random from a bag containing $5$ black balls and $3$ white balls. If the random variable $X$ denotes the number of white balls drawn, then the mean of $X$ is