If a random variable $X$ has the following probability distribution,then its variance is

$X=x$	$1$	$3$	$5$	$2$
$P(X=x)$	$3 K^2$	$K$	$K^2$	$2 K$

An urn contains $3$ black and $5$ red balls. If $3$ balls are drawn at random from the urn,the mean of the probability distribution of the number of red balls drawn is

$A$ fair die is tossed twice in succession. If $X$ denotes the number of sixes in two tosses,then the probability distribution of $X$ is given by

For a random variable $X$,if $P(X=k) = \frac{(k+1)a}{3^k}$ for $k=0, 1, 2, \ldots$,then $a = $

$A$ bag contains $4$ white and $6$ black balls. Three balls are drawn at random from the bag. Let $X$ be the number of white balls among the drawn balls. If $\sigma^{2}$ is the variance of $X$,then $100 \sigma^{2}$ is equal to.

If the probability density function of a continuous random variable $X$ is $f(x) = \frac{x^3}{3}$ for $-1 < x < 2$,and $f(x) = 0$ otherwise,then the cumulative distribution function $F(x)$ for $-1 < x < 2$ is: