3. (20%) When a power surge occurs, it can damage electrical appliances lacking a surge protector. Let's say there are three kinds of surges: small, medium and large. Each arrives as an independent Poisson Process, with rates 8 per day, 1 per day and 1 per month, respectively. In addition their probabilities of causing damage on arrival to a standard computer are 1/ 1000, 1/100 and 1/10 respectively. For the following calculations, assume each month has 30 days. (a) What is the expected number of surges per month? (b) What is the expected number of damaging surges per month? (c) What is the probability a standard computer survives a month without being damaged by a power surge? (d) What is the probability the rst surge which damages a computer is a small one