$A$ random variable $X$ takes the values $0, 1, 2, 3$ and its mean is $1.3$. If $P(X=3)=2 P(X=1)$ and $P(X=2)=0.3$,then $P(X=0)$ is

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

$A$ fair coin is tossed $2$ times. $A$ person receives $₹ X^{3}$ if he gets $X$ number of heads. His expected gain is $=$

$A$ fair die with numbers $1$ to $6$ on its faces is thrown. Let $X$ denote the number of factors of the number on the uppermost face. Then the probability distribution of $X$ is

For the following probability distribution, the standard deviation of the random variable $X$ is:
$X: 0, 1, 2$
$P(X): 0.3, 0.4, 0.3$

State whether the following table represents a probability distribution of a random variable $X$. Give reasons for your answer.

$X$	$0$	$1$	$2$
$P(X)$	$0.4$	$0.4$	$0.2$