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

A die is thrown $120$ times and getting $1$ or $5$ is considered a success. Find the mean and variance of the number of successes.

"The mean of a binomial distribution is $6$ and the standard deviation is $4$'''. Can the statement be true? Give the reason.

If one out of $10$ persons are illiterate, find the mean and standard deviation of the number of literate persons out of a total of $500$ persons.

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

A random variable $X$ has the following probability mass function

Then the value of $\lambda$ is 

Variance of the random variable $X$ is $4$. Its mean is $2$. Then $E\left(X^2\right)$ is:

The mean of a binomial distribution is $5$ and its standard deviation is $2$. Then the value of $n$ and $p$ are 

If the mean of a binomial distribution is $18$ and variance is equal to $12$. Then the value of $n+p+q$ is