The variance of the following probability distribution is:

$x$	$0$	$1$	$2$
$P(X)$	$\frac{9}{16}$	$\frac{3}{8}$	$\frac{1}{16}$

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

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

$A$ coin is tossed twice in succession. Let $X$ represent the number of tails in two tosses,then the probability distribution of $X$ is given by

The cumulative distribution function of a discrete random variable $X$ is given by the following table:

$X = x$	$-4$	$-2$	$0$	$2$	$4$	$6$	$8$	$10$
$F(X = x)$	$0.1$	$0.3$	$0.5$	$0.65$	$0.75$	$0.85$	$0.90$	$1$

Then,calculate $\frac{P(X \leqslant 0)}{P(X > 0)}$.

In a book of $250$ pages,there are $200$ typographical errors. Assuming that the number of errors per page follows the Poisson distribution,the probability that a random sample of $5$ pages will contain no typographical error is

If $X$ is a Poisson variate such that $P(X=1)=P(X=2)$,then $P(X=4)$ is equal to