a. Show that if X has a normal distribution with parameters and , then Y =

a. Show that if X has a normal distribution with parameters μ and θ, then Y = aX + b (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)]? [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?