8. Wind power distribution (15 points). The average wind speed over a certain period of time, e.g., 15min or 1hr, at a location is modeled by a Weibull distribution with cdf 8 k: 173(3) = 1 e_()\\) for 3 Z 0, and F303) = 0, otherwise, where k > 0 and A > 0 are called the shape and scale of the distribution. Note that the Exp()\\) distribution is a Special case of the Weibull distribution when k = 1. (b) The average power P generated by a wind turbine is proportional to the cube of S, i.e., P = aS for some a > 0. Find the pdf of P. You may use a tool such as Wol- fram Alpha to find derivatives. https:/ /www.wolframalpha.com/input/?i=derivative