Let Y = X? , with X ? Expo(1) and ? > 0. The distribution of Y is called the Weibull distribution with parameter ?. This generalizes the Exponential, allowing for non-constant hazard functions. Weibull distributions are widely used in statistics, engineering, and survival analysis; there is even an 800-page book devoted to this distribution: The Weibull Distribution: A Handbook by Horst Rinne. For this problem, let ? = 3.(a) Find P(Y > s + t|Y > s) for s, t > 0. Does Y have the memoryless property?(b) Find the mean and variance of Y , and the nth moment E(Y n ) for n = 1, 2, . . . .(c) Determine whether or not the MGF of Y exists.