The discrete random variable $X$ can take all possible integer values from $1$ to $k$,each with a probability $\frac{1}{k}$. Then its variance is

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

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

$X=k$	$0$	$1$	$2$	$3$	$4$
$P(X=k)$	$0.1$	$0.4$	$0.3$	$0.2$	$0$

The variance of $X$ is:

The probability of India winning a test match against West Indies is $\frac{1}{2}$. Assuming independence from match to match,the probability that in a $5$ match series India's second win occurs at the third test,is

In a hospital,on an average if there are $35$ births in a week,then the probability that there will be less than $3$ births in a day is:

$A$ class has $15$ students whose ages are $14, 17, 15, 14, 21, 17, 19, 20, 16, 18, 20, 17, 16, 19$ and $20$ years. One student is selected in such a manner that each has the same chance of being chosen and the age $X$ of the selected student is recorded. What is the probability distribution of the random variable $X$? Find the mean,variance,and standard deviation of $X$.