If two dice are thrown and if $X$ denotes the sum of the numbers that show up on the faces of the dice,then the mean of the random variable $X$ is

$A$ fair $n$ $(n > 1)$ faced die is rolled repeatedly until a number less than $n$ appears. If the mean of the number of tosses required is $\frac{n}{9}$,then $n$ is equal to

For the probability distribution given below,find $\operatorname{Var}(X)$.

$X$	$5$	$6$	$7$	$8$	$9$	$10$	$11$
$P(X=x)$	$0.07$	$0.2$	$0.3$	$k$	$0.07$	$0.04$	$0.02$

The probability that an individual suffers a bad reaction from an injection is $0.001$. The probability that out of $2000$ individuals exactly three will suffer a bad reaction is:

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:

$A$ service station manager sells gas at an average of ₹ $100$ per hour on a rainy day,₹ $150$ per hour on a dubious day,₹ $250$ per hour on a fair day,and ₹ $300$ per hour on a clear sky day. If weather bureau statistics show the probabilities of weather as follows,then his mathematical expectation is:

Weather	Clear	Fair	Dubious	Rainy
Probability	$0.50$	$0.30$	$0.15$	$0.05$