The mean of the numbers obtained on throwing a die having written $1$ on three faces,$2$ on two faces,and $5$ on one face is

$A$ person who tosses an unbiased coin gains two points for turning up a head and loses one point for a tail. If three coins are tossed and the total score $X$ is observed, then the range of $X$ is

The cumulative distribution function (c.d.f.) $F(x)$ of a discrete random variable $X$ is given by the following table:

$X$	$-3$	$-1$	$0$	$1$	$3$	$5$	$7$	$9$
$F(X)$	$0.1$	$0.3$	$0.5$	$0.65$	$0.75$	$0.85$	$0.90$	$1$

Then,find $P[X=3]$.

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

If the probability distribution of a random variable $X$ is as follows,then $P(X \leq 2) = $

$x_i$	$0$	$1$	$2$	$3$	$4$
$P(X = x_i)$	$3K$	$5K$	$3k^2$	$4k^2 + k$	$3k^2$

If the range of a random variable $X$ is $\{0, 1, 2, 3, 4, \ldots\}$ with $P(X=k) = \frac{(k+1)a}{3^k}$ for $k \geq 0$,then $a$ is equal to