Embibe Experts Solutions for Chapter: Probability Distribution, Exercise 1: Exercise 1

A pair of dice is rolled, if the outcome is a doublet, a coin is tossed. Then, the total number of outcomes for this experiment is

An experiment consists of rolling a die until a $2$ appears. Then, number of elements of the sample space corresponding to the event that the $2$ appears not later than the $k^{th}$ roll of the die is

A random variable $X$ has the following probability distribution:

A discrete random variable $X$ has the following probability distribution

The value of $C$ and the mean of the distribution are

The total lifetime (in year) of $5$ year old dog of a certain breed in a random variable whose distribution function is given by $f\left(x\right)=\left\{\begin{array}{ll}0& , \text{for} x\le 5\\ 1-\frac{25}{x^2},& \text{for} x>5\end{array}\right.$. Then the probability that such a five-year-old dog will live beyond $10$ years are

For the probability distribution given by

The standard deviation $\left(\mathrm{\sigma }\right)$ is

If the probability density function of a random variable is given by $f\left(x\right)=\left\{\begin{array}{l}k\left(1-x^2\right), 0<x<1\\ 0, \text{elsewhere}\end{array}\right.$, then the value of $k$ is

If $F\left(x\right)=\frac{1}{\mathrm{\pi }}\left(\frac{\mathrm{\pi }}{2}+{\tan }^{-1}\right)-\infty <x<\infty$ is a distribution function of a continuous variable $X,$ then $P\left(0\mathit{\le }x\mathit{\le }1\right)$ is