Question

EXAMPLE 18B The number of days needed to design a new product depends on how complicated the product is. Y is an index that measures the complication of the product. The mean of Y is 5 and the variance of Y is 12. The number of days needed to design a new product, given Y = y, has a mean of 10y and a variance of 3y Calculate the variance of the number of days needed to design a new product.

Answer 1

Let X denote the number of days required to design a new product.

We know that

Var(x) = E[Var(X Y = y)] + Var[E(X Y = y)

Now,

EXY = y) = 10y, Var(X Y = y) = 3y?

So,

Var(X) = E|3Y?]+Var10Y) = 3E(Y) + 10'Var(Y)

=3[Var(Y) + E(Y)%] + 10Var(Y) = 3/12 + 541 + 100(12) = 1311