Each month a manufacturer stocks one warehouse with good x a

Each month, a manufacturer stocks one warehouse with good x and two warehouses with good y. Monthly sales for x and y (as fractions of a full warehouse) are then random, described by the following joint density:

f(x,y) = 1-k(x+y) if x [0,1], y [0,2]

            0             else

- Suppose that goods x and y sell for $50,000 and $40,000 (per warehouse-full), respectively. For the joint density, find average total monthly revenue. Also, find Cov(X,Y) and Corr(X,Y).

Thank you!

Solution