Two cards are drawn simultaneously from a well-shuffled pack of $52$ cards. If $X$ is the random variable representing the number of queens obtained,then the value of $2 E(X) + 3 E(X^2)$ is:

If $P(X=2)=0.3, P(X=3)=0.4, P(X=4)=0.3$,then the variance of random variable $X$ is (in $.6$)

If the probability distribution of a random variable $X$ is as follows,then $k=$

$X=x$	$1$	$2$	$3$	$4$
$P(X=x)$	$2k$	$4k$	$3k$	$k$

(in $/10$)

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 $P[X=3]$.

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

If $X$ is a Poisson variate with $P(X=0)=0.8$,then the variance of $X$ is