From a bag containing $4$ white and $5$ red balls,if $3$ balls are drawn at random,then the mean of the number of red balls among the balls drawn is:

Two persons $A$ and $B$ play a game by throwing two dice. If the sum of the numbers appeared on the two dice is even, $A$ will get $\frac{1}{2}$ point and $B$ will get $\frac{1}{2}$ point. If the sum is odd, $A$ will get one point and $B$ will get no point. The arithmetic mean of the random variable of the number of points of $A$ is

The p.d.f. of a random variable $X$ is given by $f(x) = \frac{k}{\sqrt{x}}$ for $0 \leq x \leq 4$ and $f(x) = 0$ otherwise. Then $P(1 < X < 4) = $

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

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

Which of the following functions is not a probability density function $(p.d.f.)$ of a continuous random variable $X$?

$A$ random variable $X$ has the probability distribution as given below. Let $E = \{X \mid X \text{ is a prime number}\}$ and $F = \{X \mid X < 4\}$,then $P(E \cup F) = $
$\begin{array}{|c|c|c|c|c|c|c|c|c|} \hline X & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 \\ \hline P(X) & K & 2K & K^2 & 2K^2 & 5K^2 & K & K & 2K \\ \hline \end{array}$