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

$X = x$	$0$	$1$	$2$	$3$
$P(X = x)$	$\frac{1}{10}$	$\frac{2}{10}$	$\frac{3}{10}$	$\frac{4}{10}$

Then the variance of $X$ is

In a city,$10$ accidents take place in a span of $50$ days. Assuming that the number of accidents follows the Poisson distribution,the probability that three or more accidents occur 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 $X$.

$A$ random variable $X$ takes values $0, 1, 2, 3$ with probabilities $\frac{2a + 1}{30}, \frac{8a - 1}{30}, \frac{4a + 1}{30}, b$ respectively, where $a, b \in R$. Let $\mu$ and $\sigma$ respectively be the mean and standard deviation of $X$ such that $\sigma^{2} + \mu^{2} = 2$. Then $\frac{a}{b}$ is equal to:

In a communication network, $98 \%$ of messages are transmitted with no error. If a random variable $X$ denotes the number of incorrectly transmitted messages, then the probability that at most one message is transmitted incorrectly out of $500$ messages sent, is

$A$ typist claims that he prepares a typed page with typo errors of $1$ per $10$ pages. In a typing assignment of $40$ pages, if the probability that the typo errors are at most $2$ is $p$, then $e^2 p=$