If $X$ is a Poisson variate satisfying the condition $3 P(X=2)=P(X=4)$,then find $P(X=6)$.

$A$ coin is tossed three times. Let $X$ denote the number of times a tail follows a head. If $\mu$ and $\sigma^2$ denote the mean and variance of $X$, then the value of $64(\mu+\sigma^2)$ is :

$A$ random variable $X$ has the following probability distribution. For events $E = \{X \text{ is a prime number}\}$ and $F = \{X < 4\}$,what is the probability $P(E \cup F)$?

$X$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$
$P(X)$	$0.15$	$0.23$	$0.12$	$0.10$	$0.20$	$0.08$	$0.07$	$0.05$

$A$ random variate $X$ takes the values $0, 1, 2, 3$ and its mean is $1.3$. If $P(X=3) = 2 P(X=1)$ and $P(X=2) = 0.3$,then $P(X=0)$ is equal to:

$A$ 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

$A$ die is rolled. If $X$ denotes the number of positive divisors of the outcome,then the range of the random variable $X$ is