If the mean of a Poisson distribution is $\frac{1}{2}$, then the ratio of $P(X=3)$ to $P(X=2)$ is

The probability distribution of a random variable $X$ is given by:

$X = x$	$1$	$2$	$3$	$4$
$P(X = x)$	$1/10$	$2/10$	$3/10$	$4/10$

Then the cumulative distribution function (c.d.f.) $F(x)$ of $X$ is given by:

If the probability distribution of a random variable $X$ is given by the following table,then $F(0) =$ . . . . . .

$x_i$	$-2$	$-1$	$0$	$1$	$2$
$P(X = x_i)$	$0.2$	$0.5$	$0.15$	$0.25$	$0.1$

Find the probability distribution of the number of heads in two tosses of a coin.

The range of a random variable $X$ is $\{0, 1, 2\}$. If $P(X = 0) = 3c^3$, $P(X = 1) = 4c - 10c^2$, and $P(X = 2) = 5c - 1$, then find $P(0 < X \le 2)$.

If $m$ and ${\sigma ^2}$ are the mean and variance of a random variable $X$,whose distribution is given by:

$X=x$	$0$	$1$	$2$	$3$	$4$
$P(X=x)$	$\frac{1}{3}$	$\frac{1}{2}$	$0$	$\frac{1}{6}$	$0$

,then: