If the probability function of a random variable $X$ is given by $P(X=j) = \frac{1}{2^j}$ for $j = 1, 2, 3, \ldots, \infty$,then the variance of $X$ is:

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

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

Then,find the value of $\frac{P[X=-3]}{P[X < 0]}$.

At a telephone enquiry system,the number of phone calls regarding relevant enquiries follows a Poisson distribution with an average of $5$ phone calls during $10$-minute time intervals. The probability that there is at most one phone call during a $10$-minute time period is:

The probability function of a discrete random variable $X$ is given by $P(X=r)=K r^2$, where $r=-2,-1,0,1,2,3$ and $K$ is a constant. The sum of the variance of $X$ and the square of the mean of $X$ is

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:

$A$ random variable $X$ has the probability distribution given below. Its variance is:

$X$	$1$	$2$	$3$	$4$	$5$
$P(X=x)$	$K$	$2K$	$3K$	$2K$	$K$