Suppose the random variable X takes on only two values, according to the probability distribution given below. Suppose X is a discrete random variable with mean mX and variance s2 X. Let Y be a linear...

Suppose the random variable X takes on only two values, according to the probability distribution given below.

Suppose X is a discrete random variable with mean mX and variance s2 X. Let Y be a linear function of X, such that Y 5 aX 1 b, where a and b are constants. Find the mean and variance of Y in terms of mX and s2 X.

Suppose X is a discrete random variable that takes on a finite number of values. Prove the variance computation formula. That is, show that

Suppose X is a discrete random variable with mean mX and variance s2 X. Let Y be defined in terms of X by

Find the mean, variance, and standard deviation of Y.