In a pack of 52 playing cards, two cards are drawn at random simultaneously. If the number of black cards drawn is a random variable, find the values of the random variable and number of points in its inverse images.

Two balls are chosen randomly from an urn containing 6 red and 8 black balls. Suppose that we win Rs. 15 for each red ball selected and we lose Rs. 10 for each black ball selected. X denotes the winning amount, then find the values of X and number of points in its inverse images.

A six sided die is marked '2' on one face, '3' on two ofits faces, and '4' on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find the values of the random variable and number of points in its inverse images.

The probability density function of X is 
\(f(x)=\left\{\begin{array}{cc} x & 0
find P(0.2 ≤ X< 0.6) 

The probability density function of X is 
\(f(x)=\left\{\begin{array}{cc} x & 0
find P(0.5≤X<1.5)

For the random variable X with the given probability mass function as below, find the mean and variance \(f(x)= \begin{cases}2(x-1) & 1

The probability density function random variable X is given by \(f(x)=\begin{cases} \begin{matrix} { 16xe }^{ -4x } & for\quad x>0 \end{matrix} \\ \begin{matrix} 0 & for\quad x\le 0 \end{matrix} \end{cases}\) find the mean and variance of X.

The probability that Mr.Q hits a target at any trial is \(\frac { 1 }{ 4 } \). Suppose he tries at the target 10 times. Find the probability that he hits the target
(i) exactly 4 times
(ii) at least one time.

Suppose two coins are tossed once. If X denotes the number of tails,
(i) write down the sample space
(ii) find the inverse image of 1
(iii) the values of the random variable and number of elements in its inverse images

Two fair coins are tossed simultaneously (equivalent to a fair coin is tossed twice). Find the probability mass function for number of heads occurred.