The number / of earthquakes in a highly seismic area follows a Poisson distri- bution with parameter A = 1/2 per year. The cost of damages in hundreds of thousands of dollars for each earthquake is a random variable with pdf: f(x) = 9 The costs of damages for the earthquakes are independent of each other, and are independent of N. 1. Find the average of the cost of damages per earthquake. 2. Find the variance of the cost of damages per earthquake. 3. By conditioning on N, find the average and variance of the cost X of damages due to all earthquakes in a year. 4. Let Y = cos(N), where N is as above. Find the range and the mean of Y. What is P(Y = 1)