The number of cases , , arriving at hospital's has a Poisson distribution with rate of 16 per night. Doctor's basic shift is 12 hours. Each case on shift will take an extra of an hour. Assume that a single doctor sees all cases.

Part A: Let represent the length of a doctor's shift. Write an equation for in terms of .

My answer is : . I think it is correct.

Part B: Calculate expected value and variance of Y.

This part I'm totally lost. What should I do?

Please help me. Thank you.