$A$ person throws an unbiased die. If the number shown is even,he gains an amount equal to the number shown. If the number is odd,he loses an amount equal to the number shown. Then his expectation is ₹.

Let $X$ denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of $X$.

If the probability that the random variable $X$ takes the value $x$ is given by $P(X=x) = k(x+1)3^{-x}$,for $x = 0, 1, 2, 3, \ldots$,where $k$ is a constant,then $P(X \geq 3)$ is equal to

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

$X$	$0$	$1$	$2$
$P(X)$	$\frac{25}{36}$	$k$	$\frac{1}{36}$

If the mean of the random variable $X$ is $\frac{1}{3}$,then the variance is:

For the following probability distribution,find the expected value of $X$:

$x$	$0$	$1$	$2$	$3$	$4$	$5$
$P(x)$	$k$	$0.3$	$0.15$	$0.15$	$0.1$	$2k$

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