In a Poisson distribution, if $P(X = 2)$ is twice $P(X = 1)$, then the standard deviation of the distribution is:

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 $E(x)$.

The distribution of a random variable $X$ is given below:

$X=x$	$1$	$2$	$3$	$4$
$P(X=x)$	$\frac{2}{20}$	$\frac{4}{20}$	$\frac{6}{20}$	$\frac{8}{20}$

Then,the standard deviation of $X$ is

When an unfair dice is thrown,the probability of getting a number $k$ on it is $P(X=k)=k^2 P$,where $k=1, 2, 3, 4, 5, 6$ and $X$ is the random variable denoting a number on the dice,then the mean of $X$ is

Suppose three coins are tossed simultaneously. If $X$ denotes the number of heads,then the probability distribution of $X$ is:

If $X$ is a Poisson random variate with mean $3$,then $P(|X-3| < 2) =$