If two cards are drawn randomly from a pack of $52$ playing cards,then the mean of the probability distribution of the number of kings is

For the random variable $X$ with the probability distribution given by the table:

$X = x$	$0$	$1$	$2$	$3$
$P(X = x)$	$K$	$K + \frac{1}{7}$	$2K$	$\frac{2}{5}$

The mean of $X$ is:

$5$ persons entered a lift cabin on the ground floor of a $7$-floor house. Suppose that each of them independently and with equal probability can leave the cabin at any floor beginning with the first. The probability of all the $5$ persons leaving the cabin at different floors is

Let $X$ denote the number of hours you study during a randomly selected school day. The probability that $X$ can take the values $x$ has the following form,where $k$ is some unknown constant.
$P(X=x) = \begin{cases} 0.1, & \text{if } x=0 \\ kx, & \text{if } x=1 \text{ or } 2 \\ k(5-x), & \text{if } x=3 \text{ or } 4 \\ 0, & \text{otherwise} \end{cases}$
Find the value of $k$.

For a Poisson variate $X$,if $P(X=2)=3 P(X=3)$,then the mean of $X$ is:

Three balls are drawn at random from a bag containing $5$ blue and $4$ yellow balls. Let the random variables $X$ and $Y$ respectively denote the number of blue and yellow balls. If $\bar{X}$ and $\bar{Y}$ are the means of $X$ and $Y$ respectively,then $7 \bar{X} + 4 \bar{Y}$ is equal to ..........