If $X$ is a Poisson variate with $P(X=0)=0.8$,then the variance of $X$ is

Let $X$ denote the sum of the numbers obtained when two fair dice are rolled. Find the variance and standard deviation of $X$.

Which of the following cannot be a valid assignment of probabilities for outcomes of sample space $S = \{\omega_{1}, \omega_{2}, \omega_{3}, \omega_{4}, \omega_{5}, \omega_{6}, \omega_{7}\}$?

Outcome	$\omega_{1}$	$\omega_{2}$	$\omega_{3}$	$\omega_{4}$	$\omega_{5}$	$\omega_{6}$	$\omega_{7}$
Probability	$-0.1$	$0.2$	$0.3$	$0.4$	$-0.2$	$0.1$	$0.3$

If the probability distribution of a random variable $X$ is given by the following table,then $F(0) =$ . . . . . .

$x_i$	$-2$	$-1$	$0$	$1$	$2$
$P(X = x_i)$	$0.2$	$0.5$	$0.15$	$0.25$	$0.1$

$15$ coupons are numbered from $1$ to $15$. Seven coupons are selected at random with replacement. What is the probability that the maximum number on the selected coupons is $9$?

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

$X=x$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$
$P(X=x)$	$0$	$K$	$2K$	$2K$	$3K$	$K^2$	$2K^2$	$7K^2+K$

Then,$P(0 < X < 5)$ is equal to: