Tom and Huck are painting a fence together. Tom and Huck both start paintingat the same time, but lazy Huck stops working after Y hours, where the randomvariable Y is uniform on (0, 1). Diligent Tom then finishes the job at the X, wherethe conditional distribution of X is uniform on (Y, 1).

(a) What is the expected time that Tom works?

(b) What is variance of the time that Tom works?

(c) If Huck and Tom are paid a total of $10 to do the job, and they split themoney according to the length of time each one works, what is the expectedamount that Tom gets?