During an eight-hour shift, the proportion of time y that a sheetmetal stamping machine is down for maintenance or repairs has a beta distribution with α = 1 and β = 2. that is f(y) =    2(1 − y), 0 ≤ y ≤ 1, 0, elsewhere. the cost (in hundreds of dollars) of this downtime, due to lost production and cost of maintenance and repair, is given by c = 10 + 20y + 4y 2 . find the mean and variance of c.