$A$ fair $n$-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 $n=$ (where $n \in N$ ).

$A$ random variable $X$ has the following distribution.

$X = x_{i}$	$-2$	$-1$	$0$	$1$	$2$	$3$
$P(X = x_{i})$	$0.1$	$k$	$0.2$	$2k$	$3k$	$k$

Then the variance of this distribution is

For the following probability distribution,find the $Var(X)$.

$X$	$-2$	$-1$	$0$	$1$	$2$	$3$
$P(X)$	$0.1$	$0.2$	$0.2$	$0.3$	$0.15$	$0.05$

(Given : $(0.25)^2 = 0.0625$,$(0.35)^2 = 0.1225$,$(0.45)^2 = 0.2025$)

If a die is thrown at random,then the expectation of the number on it is

The value of the constant $c$,so that $P(x)=c\left(\frac{2}{3}\right)^{x}$,$x=1,2,3, \ldots$ is the probability distribution function of a discrete random variable $X$ is

Two persons $A$ and $B$ play a game by throwing two dice. If the sum of the numbers appeared on the two dice is even,$A$ will get $\frac{1}{2}$ point and $B$ will get $\frac{1}{2}$ point. If the sum is odd,$A$ will get one point and $B$ will get no point. The arithmetic mean of the random variable of the number of points of $A$ is