If $x$ is a random variable with $PMF$ as follows: $P(X = x) = \begin{cases} \frac{5}{16}, & x = 0, 1 \\ \frac{kx}{48}, & x = 2 \\ \frac{1}{4}, & x = 3 \end{cases}$ then find $E(x)$.

If $X$ is a random variable with the following probability distribution:

$X=x$	$-3$	$6$	$9$
$P(X=x)$	$\frac{1}{6}$	$\frac{1}{2}$	$\frac{1}{3}$

Then the variance of $X$ is:

If a random variable $X$ has the probability distribution given by $P(X=0)=3C^3$,$P(X=2)=5C-10C^2$ and $P(X=4)=4C-1$,then the variance of that distribution is

Three defective oranges are accidentally mixed with seven good ones and on looking at them,it is not possible to differentiate between them. Two oranges are drawn at random from the lot. If $x$ denotes the number of defective oranges,then the variance of $x$ is:

$A$ random variable $X$ has the following probability distribution:

$X$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P(X)$	$0$	$k$	$2k$	$2k$	$3k$	$k^2$	$2k^2$	$7k^2+k$

Determine $k$.

The discrete random variables $X$ and $Y$ are independent from one another and are defined as $X \sim B(16, 0.25)$ and $Y \sim P(2)$. Then the sum of the variances of $X$ and $Y$ is