a. Show that if X has a normal distribution with parameters μ and σ , 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)]? [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?
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