Linear Transformations of Normal Random Variables are also N

Linear Transformations of Normal Random Variables are also Normal Let X N(mu, sigma^2) and a, b K. Show that Y = aX + b is also a normal random variable. With what parameters? Compute Fy(y) = P(Y LE y) = P(X LE y) = integrate.... Suppose that the temperature in some town on some randomly chosen day follows the normal distribution with mean 15 and standard deviation 5, when measured in degree C. What can you say about the temperature in degreeF? degreeF = 32 + (9/5) degree C.

Solution