Find the mean and standard deviation of each of the following probability distribution :

$x_i$	$0$	$1$	$2$	$3$	$4$	$5$
$p_i$	$\frac{1}{6}$	$\frac{5}{18}$	$\frac{2}{9}$	$\frac{1}{6}$	$\frac{1}{9}$	$\frac{1}{18}$

A discrete random variable $X$ has the probability distribution given below:

Find the value of $k$.

A discrete random variable $X$ has the probability distribution given below:

Determine the mean of the distribution when $k=\frac{1}{3}$.

Find the mean variance and standard deviation of the following probability distribution

where $p+q=1$ .