8In a daily production of certain kind of rope the number of

(8)In a daily production of certain kind of rope, the number of defects per foot Y b assumed to have a Poisson distribution with mean lambda = 2. The profit per foot when t he rope is sold is given by X, where X = 50 - 2Y - Y^2 The the expected profit per foot.

Solution

First let us calculate E(Y) and E(Y²)

E(Y) = Mean of Poisson distribution with lemda 2 = 2

VAriance(Y) = 2

E(Y²) = 2+2^2 =6

Expected value of profit = E(50-2y-y²)

= 50-2E(Y)-E(Y²)

= 50 -4-6

= 40