The discrete random variables $X$ and $Y$ are independent from one another and are defined as $X \sim B(16, 0.25)$ and $Y \sim P(2)$. Then the sum of the variances of $X$ and $Y$ is

$15$ 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 $9$?

Find the probability distribution of the number of successes in two tosses of a die,where a success is defined as 'six appears on at least one die'.

$A$ fair die is tossed twice in succession. If $X$ denotes the number of fours in $2$ tosses,then the probability distribution of $X$ is given by

The c.d.f. $F(x)$ associated with the p.d.f. $f(x)$ is given by:
$f(x) = \begin{cases} 12x^2(1-x), & \text{if } 0 < x < 1 \\ 0, & \text{otherwise} \end{cases}$

$A$ boy rolls a die once. If an even number appears,the number of chocolates the boy gets is equal to two more than the number that appeared. If an odd number appears on the die,the number of chocolates he gets is equal to three more than the number that appeared. If a random variable $X$ represents the number of chocolates the boy receives,then the range of $X$ is: