(3) Edwin catches trout at times of a Poisson process with rate 3 per hour. Suppose that the trout weigh an average of 4 pounds with a standard deviation of 2 pounds. Find the mean and variance of the total weight of fish he catches in 2 hours.
(4) A certain type of light bulb has a lifetime that is exponential with a rate of λ. Suppose that there are three light bulbs which are not replaced when they burn out. Show that the expected amount of time for all three bulbs to burn out is (1/ 3λ) + (1/ 2λ) + (1/ λ).