Suppose X is the number of tails occurred when three fair coins are tossed once simultaneously. Find the values of the random variable X and number of points in its reverse images.

Three fair coins are tossed simultaneously. Find the probability mass function for number of heads occurred.

A six sided die is marked '1' on one face, '3' on two of its faces, and '5' on remaining three faces. The die is thrown twice. If X denotes the total score in two throws, find
(i) the probability mass function
(ii) the cumulative distribution function
(iii) P(4 ≤ X < 10)
(iv) P(X ≥ 6)

Find the probability mass function and cumulative distribution function of number of girl child in families with 4 children, assuming equal probabilities for boys and girls.

The probability density function of X is given by \(f(x)=\begin{cases} \begin{matrix} kxe^{ -2x } & forx>0 \end{matrix} \\ \begin{matrix} 0 & for\quad x\le 0 \end{matrix} \end{cases}\) Find the value of k.

The probability density function of X is given
\(f(x)=\begin{cases} \begin{matrix} { Ke }^{ \frac { -x }{ 3 } } & \begin{matrix} for & x>0 \end{matrix} \end{matrix} \\ \begin{matrix} 0 & \begin{matrix} for & x\le 0 \end{matrix} \end{matrix} \end{cases}\)
Find
(i) the value of k
(ii) the distribution function.
(iii) P(X <3)
(iv) P(5 ≤X)
(v) P(X ≤ 4)

For the random variable X with the given probability mass function as below, find the mean and variance 

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

A lottery with 600 tickets gives one prize of Rs. 200, four prizes of Rs.100, and six prizes of Rs. 50. If the ticket costs is Rs. 2, find the expected winning amount of a ticket.

Compute P(X = k) for the binomial distribution, B(n, p) where
\(P(X=10)=\left( \begin{matrix} 10 \\ 4 \end{matrix} \right) \left( \cfrac { 1 }{ 5 } \right) ^{ 4 }\left( 1-\cfrac { 1 }{ 5 } \right) ^{ 10-4 }\)

Compute P(X = k) for the binomial distribution, B(n, p) where
n = 9, \(p=\frac { 1 }{ 2 } \), k = 7

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.

A retailer purchases a certain kind of electronic device from a manufacturer. The manufacturer, indicates that the defective rate of the device is 5%. The inspector of the retailer randomly picks 10 items from a shipment. What is the probability that there will be
(i) at least one defective item
(ii) exactly two defective items.

If X~ B(n, p) such that 4P(X = 4) = P(X = 2) and n = 6. Find the distribution, mean and standard deviation of X.

In a binomial distribution consisting of 5 independent trials, the probability of 1 and 2 successes are 0.4096 and 0.2048 respectively. Find the mean and variance of the random variables.