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.
I'm afraid you have completely misunderstood. Let me be crystal clear: Y = aX + b.
Is it clear to you what the random variables X and Y represent in your problem? It should be because the question defines them.
Is it clear to you what you're trying to find? You're trying to solve for E(Y) and Var(Y).
Is it clear to you that you're essentially given the value of E(X) and Var(X) ....?