The increase in demand for electric power in millions of kilowatt hours over the next 2 years in a certain area is a random variable X with density f(z) = 2*/64,0 < z 4. Assume f(x) = 0 elsewhere. (a) (5 points) Why is this a legitimate density? (b) (10 points) Find E(X) and Var(X). (c) (5 points) The area only has the capacity to generate an additional 3 million kilowatt hours. What is the probability that demand will exceed supply? (d) (5 points) Suppose in another area the increase in demand for electric power is Y = 2.5X. Calculate the expected combined increase in demand for electric power across both areas and the variance of the this combined demand.