6.10 The proportion of time X that an industrial robot is in operation during a 40-hour work week is a random variable with probability density function a Find E(X ) and V(X ).

b For the robot under study, the profit Y for a week is given by Find E(Y ) and V(Y ).

c Find an interval in which the profit should lie for at least 75% of the weeks that the robot is in use. [Hint: Use Tchebysheff’s theorem.]