R D Sharma Solutions for Chapter: Mean and Variance of a Random Variable, Exercise 2: EXERCISE

Find the mean and standard deviation of the following probability distribution:

Find the mean and standard deviation of the following probability distributions:

A discrete random variable $X$ has the probability distribution given below:

Find the value of $k$.

A discrete random variable $X$ has the probability distribution given below:

Determine the mean of the distribution when $k=\frac{1}{3}$.

A die is tossed twice. A 'success' is getting an odd number on a toss. Find the variance of the number of successes.

A box contains $13$ bulbs, out of which $5$ are defective. $3$ bulbs are randomly drawn, one by one without replacement, from the box. Find the probability distribution of the number of defective bulbs.

In roulette, Figure, the wheel has $13$ numbers $0, 1, 2, ...., 12$ marked on equally spaced slots. A player sets $\mathrm{Rs} 10$ on a given number. He receives $\mathrm{Rs} 100$ from the organiser of the game if the ball comes to rest in this slot; otherwise he gets nothing. If $X$ denotes the player's net gain/loss, find $E\left(X\right)$.

An urn contains $5$ red and $2$ black balls. Two balls are randomly drawn, without replacement. Let $X$ represent the number of black balls drawn. What are the possible values of $X$? Is $X$ a random variable ? If yes, then find the mean and variance of $X$.