Probability Distribution of a Random Variate

A probability distribution of random variable $\mathrm{X}$ is given by

Then the value of $\mathrm{E}(4\mathrm{x}+3)$ is

A player tosses two coins if two heads appears he wins Rs. $4,$ if one head appears he wins Rs. $2$, but if two tails appears he loses Rs. $3$. Find the expected sum of money he wins?

The p.d.f. of a continuous random variable $\mathrm{X}$ is given by $f\left(x\right)=\left\{\begin{array}{ll}\frac{x}{2},& 0<x<2\\ 0,& \text{ elsewhere }\end{array}\right.$. Then its mean is 

If the probability density function of a continuous random variable $\mathrm{X}$ is given by $\mathrm{f}\left(\mathrm{x}\right)=\left\{\begin{array}{cc}\frac{\mathrm{k}(1-{\mathrm{x}}^2)}{4}& 0<\mathrm{x}<1\\ 0& \mathrm{elsewhere}\end{array}\right.$, then we get $\mathrm{E}(\mathrm{X}=\mathrm{x})=\frac{3}{k}$. Find the value of $k$.

A random variable $\mathrm{X}$ has the following probability distribution.

Then, $\mathrm{P}(1\le \mathrm{X}\le 4)$ is

If a continuous random variable $X$ has probability density function given by $f\left(x\right)=\{\begin{array}{cl}12A{x}^5,& 0<x<1\\ 0,& \text{otherwise}\end{array}$ then the value of $A$ is 

If $\mathrm{Var}\left(\mathrm{X}\right)=2$ then $\mathrm{E}\left(\mathrm{Var}\right(4\mathrm{X}+3\left)\right)=\mathrm{E}\left(32\right)$.

If the variance of a random variable $\mathrm{X}$ is $8$ and its mean is $2$ then the expectation of $X^2$ is 

In an entrance examination student has answered all the $120$ questions. Each question has $4$ options and only one option is correct. A student gets one mark for correct answer and looses $\frac{1}{2}$ marks for wrong answer. What is the expectation of a mark scored by a student if he chooses the answer to each question at random?

A discrete random variable has the following probability distribution function

Then, we have $\mathrm{P}(3<\mathrm{X}<7)=\frac{11}{k}$. Find the value of $k$.

The following is a probability density function, $\mathrm{f}\left(\mathrm{x}\right)=5{\mathrm{x}}^4$ for$0<\mathrm{x}<1$.

A probability distribution of random variable $\mathrm{X}$ is given by

Find $\mathrm{E}(2\mathrm{x}+5)$.

If three coins are tossed then the variance of the number of heads is

A random variable $\mathrm{X}$ has $\mathrm{E}\left(\mathrm{X}\right)=\frac{1}{2},\mathrm{E}\left({\mathrm{X}}^2\right)=\frac{1}{2}$, find its standard deviation.

Given $\mathrm{E}(\mathrm{X}+\mathrm{C})=8$ and $\mathrm{E}(\mathrm{X}-\mathrm{C})=12$ then $\mathrm{C}$ is equal to

If the probability mass function of $\mathrm{X}$ is given by the following table 

If $f\left(x\right)=\left\{\begin{array}{cl}\frac{x^2}{k}& 0\le x\le 3\\ 0& \text{ elsewhere }\end{array}\right.$is the probability density function of a continuous random variable $X$ then the value of $k$ is

$\mathrm{Var}(4\mathrm{X}-3)=4\mathrm{Var}\left(\mathrm{X}\right)+3$

If the variance of a random variable $\mathrm{X}$ is $4$ and its mean is $2$ then $\mathrm{E}\left({\mathrm{X}}^2\right)$ is 

Find the mean of the number of tails when three coins are tossed simultaneously.