Find the mean and variance of the random variable Y.

Question

Let X be a random variable. Consider a random variable Y = g(X) = (X-µ)/σ, where μ and σ are the mean and standard deviation of X, respectively. Find the mean and variance of the random variable Y.

Answer 1

Y is the Z score, which has mean of zero and standard deviation & variance = 1

X could have any real number for mean and any positive number for the standard deviation