66.

a. Show that if X has a normal distribution with parameters m and s, then YaXb (a linear function of X) also has a normal distribution. What are the parameters of the distribution of Y [i.e., E(Y) and V(Y)]? [Hint:Write the cdf of Y, P(Y y), as an integral involving the pdf of X, and then differentiate with respect to y to get the pdf of Y.]

b. If when measured in C, temperature is normally distributed with mean 115 and standard deviation 2, what can be said about the distribution of temperature measured in F?