$A$ discrete random variable $X$ takes values $10, 20, 30,$ and $40$,with probabilities $0.3, 0.3, 0.2,$ and $0.2$ respectively. Then the expected value of $X$ is

$A$ box contains $6$ pens,$2$ of which are defective. Two pens are taken randomly from the box. If random variable $x$ represents the number of defective pens obtained,then the standard deviation of $x$ is:

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

$A$ random variable $X$ has the following probability distribution:

$X$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P(X)$	$0$	$k$	$2k$	$3k$	$3k^2$	$k^2$	$2k^2$	$7k^2+k$

Determine $P(X < 3)$. (in $/10$)

If the probability function of a discrete random variable $X$ is $P(X=r) = r/k$ for $r = 1, 2, 3, 4, 5$, then $P(X=2 \text{ or } X=k/3)$ is equal to:

If the probability mass function (p.m.f.) is given by $P(X) = k \binom{4}{x}$ for $x = 0, 1, 2, 3, 4$ and $k > 0$,and $P(X) = 0$ otherwise,then the value of $k$ is: