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

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

An urn contains $3$ black and $5$ red balls. If $3$ balls are drawn at random from the urn,the mean of the probability distribution of the number of red balls drawn is

$A$ boy rolls a die once. If an even number appears,the number of chocolates the boy gets is equal to two more than the number that appeared. If an odd number appears on the die,the number of chocolates he gets is equal to three more than the number that appeared. If a random variable $X$ represents the number of chocolates the boy receives,then the range of $X$ is:

If a discrete random variable $X$ has the probability distribution as follows:

$X = x$	$0$	$1$	$2$	$3$
$P(X = x)$	$k$	$3k$	$3k$	$k$

Then $Var(X) = $

$A$ die is loaded in such a way that each odd number is twice as likely to occur as each even number. If $E$ is the event that a number greater than or equal to $4$ occurs on a single toss of the die,then $P(E)$ is equal to:

Two dice are rolled. If a random variable $X$ denotes the sum of the numbers on them and $\mu$ denotes the mean of $X$,then $\mu+P(X < 5)+P(X>9)+P(X=7)=$