In a Poisson distribution with unit mean,calculate the value of $\sum_{x=0}^{\infty} |x-\bar{x}| P(X=x)$,where $\bar{x}$ is the mean of the distribution.

The range of a random variable $X$ is $\{0, 1, 2\}$. If $P(X=0) = 3C^3$,$P(X=1) = 4C - 10C^2$,and $P(X=2) = 5C - 1$,then the value of $C$ is

The probability distribution of a random variable $X$ is given by the following table:

$X = x$	$1$	$2$	$3$	$\dots$	$n$
$P(X = x)$	$\frac{1}{n}$	$\frac{1}{n}$	$\frac{1}{n}$	$\dots$	$\frac{1}{n}$

Then $\operatorname{Var}(X) = $

The following table shows the probability distribution of smart phones sold in a shop per day:

Number of smart phones $(x)$	$0$	$1$	$2$	$3$	$4$	$5$
Probability $(P(x))$	$k$	$0.3$	$0.15$	$0.15$	$0.1$	$2k$

Then $E(x) = ?$

In a Poisson distribution, if $\frac{P(X=5)}{P(X=2)}=\frac{1}{7500}$ and $\frac{P(X=5)}{P(X=3)}=\frac{1}{500}$, then the mean of the distribution is

$A$ 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