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**kleenex** The number of cases ,$\displaystyle X$, 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 $\displaystyle 1/8$ of an hour. Assume that a single doctor sees all cases.

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

My answer is :$\displaystyle Y=12+X/8$. 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.