$A$ coin is biased so that the head is $3$ times as likely to occur as tail. This coin is tossed until a head or three tails occur. If $X$ denotes the number of tosses of the coin,then the mean of $X$ is

$A$ random variable $X$ has the probability distribution given below. Its variance is:

$X$	$1$	$2$	$3$	$4$	$5$
$P(X=x)$	$K$	$2K$	$3K$	$2K$	$K$

From a lot of $10$ items,which include $3$ defective items,a sample of $5$ items is drawn at random. Let the random variable $X$ denote the number of defective items in the sample. If the variance of $X$ is $\sigma^2$,then $96 \sigma^2$ is equal to....................

The p.m.f. of a random variable $X$ is $P(x) = \begin{cases} \frac{2x}{n(n+1)}, & x = 1, 2, 3, \ldots, n \\ 0, & \text{otherwise} \end{cases}$,then $E(X)$ is

$A$ random variable $X$ has the following probability distribution:
$X$: $1, 2, 3, 4$
$P(X)$: $0.2, 0.4, 0.3, 0.1$
The mean and variance of $X$ are respectively:

If $X$ is a Poisson variate such that $\alpha = P(X=1) = P(X=2)$, then $P(X=4)$ is equal to