For a certain section of pine forest, the number Y of diseased trees per acre has a Poisson distribution with mean lambda=10. The disased trees are sprayed with an insecticide at a cost of 3 dollars per tree, plus a fixed overhead cost for equipment rental of 50 dollars. Letting C denote the total spraying cost for a randomly selected acre, find the expected value and variance for C.
isnt the expected value and variance just lambda which is 10 why does the answer says they are E(C)=80 and Var(C)=90?
Best Answer
What you've pointed out is that the expectation and variance of $Y$ are both $10$. But, you weren't asked to compute the expectation and variance of $Y$ -- you were asked to compute them for $C$.
Try to start by writing $C$ as a function of $Y$.