If a discrete random variable $X$ takes the values $1, 2, 3, 4$ such that $2P(X = 1) = 3P(X = 2) = P(X = 3) = 5P(X = 4)$, then $P(X = 4) = ...$ (in $61$)

If $X$ is a Poisson variate with $P(X=0)=0.8$, then the variance of $X$ 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 p.d.f. of a random variable $x$ is given by $f(x) = \frac{1}{4a}$ for $0 < x < 4a$ $(a > 0)$ and $f(x) = 0$ otherwise. If $P(x < \frac{3a}{2}) = k P(x > \frac{5a}{2})$,then $k = . . . . . .$

$A$ fair $n$ $(n > 1)$ faced die is rolled repeatedly until a number less than $n$ appears. If the mean of the number of tosses required is $\frac{n}{9}$,then $n$ is equal to

$A$ coin is biased so that the head is $3$ times as likely to occur as tail. If the coin is tossed twice,find the probability distribution of number of tails.