8 An environmental engineer at a large gravel company models

8. An environmental engineer at a large gravel company models Y , the monthly gravel sales (in thousands of tons) as a random variable with probability distribution function (pdf) fY (y) = ( 140y 3 (1 y) 3 , 0 < y < 1 0, otherwise.

(a) Compute E(Y ) and V (Y ).

(b) Suppose that monthly revenue (in $100, 000) from gravel sales is given by R = 10(1 Y ).

Find the mean and standard deviation of R.

Solution