M L Aggarwal Solutions for Chapter: Probability, Exercise 9: EXERCISE

Find the mean of the Binomial distribution $B\left(8, \frac{1}{4}\right)$.

Find the expectation of number of heads in 20 tosses of a fair coin.

The mean and the variance of a binomial distribution are $4$ and $2$ respectively. The probability of exactly one success is $\frac{k}{32}$. Find the value of $k$.

The mean and the variance of a binomial distribution are $4$ and $2$ respectively. The probability of exactly two successes is $\frac{k}{64}$ then find the value of $k$.

If $X$ follows a binomial distribution with mean $3$ and variance $\frac{3}{2}$, then $P(X\le 5)=\frac{k}{64}$.  Find the value of $k$.

If the sum of the mean and the variance of a binomial distribution for $54$ trials is $30$, then find the distribution.

If the sum of the mean and the variance of a binomial distribution for $5$ trials is $1.8$, then find the distribution.

If the sum and the product of the mean and variance of a binomial distribution are $24$ and $128$ respectively, then find the distribution.