The probability mass function of a random variable $X$ is given by $P[X = r] = \begin{cases} \frac{^n C_r}{32}, & r = 0, 1, 2, \dots, n \\ 0, & \text{otherwise} \end{cases}$. Then,$P[X \leq 2] = $

If the probability density function of a continuous random variable $X$ is $f(x) = \frac{x^3}{3}$ for $-1 < x < 2$,and $f(x) = 0$ otherwise,then the cumulative distribution function $F(x)$ for $-1 < x < 2$ is:

$A$ fair coin is tossed four times. $A$ person wins $Rs. 1$ for each head and loses $Rs. 1.50$ for each tail that turns up. From the sample space,calculate the different amounts of money one can have after four tosses and the probability of having each of these amounts.

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

Two persons $A$ and $B$ play a game by throwing two dice. If the sum of the numbers appeared on the two dice is even,$A$ will get $\frac{1}{2}$ point and $B$ will get $\frac{1}{2}$ point. If the sum is odd,$A$ will get one point and $B$ will get no point. The arithmetic mean of the random variable of the number of points of $A$ is

From a bag containing $4$ white and $5$ red balls,if $3$ balls are drawn at random,then the mean of the number of red balls among the balls drawn is: