Question

In the daily production of a certain kind of rope, the number of defects per foot

Y is assumed to have a Poisson distribution with mean A = 2. The profit per foot

when the rope is sold is given by X, where X = 50 - 2Y - y2. Find the expected

profit per foot

Answer 1

From the problem statement, $E[Y]=2$ .

The Poisson distribution with parameter λ has mean λ and variance λ, so we have

$\lambda=2$ and $V[Y]=2$ . Now $E[Y^2]=V[Y]+E[Y]^2=2+2^2=6$ .

Using linearity of expectation, 

$E[X]=E[50-2Y-Y^2]=E[50]-2E[Y]-E[Y^2]=50-2*2-6=40$