R S Aggarwal Solutions for Exercise 1: EXERCISE

Find the mean $\left(\mu \right)$, variance $\left({\sigma }^2\right)$ and standard deviation $\left(\sigma \right)$ for each of the following probability distributions:

Find the mean $\left(\mu \right)$, variance $\left({\sigma }^2\right)$ and standard deviation $\left(\sigma \right)$ for each of the following probability distributions:

Find the mean $\left(\mu \right)$, variance $\left({\sigma }^2\right)$ and standard deviation $\left(\sigma \right)$ for each of the following probability distributions:

Three balls are drawn simultaneously from a bag containing $5$ white and $4$ red balls. Let $X$ be the number of red balls drawn. Find the mean and variance of $X.$

Two cards are drawn without replacement from a well-shuffled deck of $52$ cards. Let $X$ be the number of face cards drawn. Find the mean and variance of $X$.

Two cards are drawn one by one with replacement from a well-shuffled deck of $52$ cards. Find the mean and variance of the number of aces.

Three cards are drawn successively with replacement from a well – shuffled deck of $52$ cards. A random variable $X$ denotes the number of hearts in the three cards drawn. Find the mean and variance of $X$.

Five defective bulbs are accidentally mixed with $20$ good ones. It is not possible to just look at a bulb and tell whether or not it is defective. Find the probability distribution from this lot.

“Note: This question given in the book seems to have error and the modified question should be as given below.”

Five defective bulbs are accidentally mixed with $20$ good ones. It is not possible to just look at a bulb and tell whether or not it is defective. Find the probability distribution if four bulbs are drawn from this lot.