In: Statistics and Probability
During an eight-hour shift, the proportion of time Y that a sheet-metal 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 + 30Y + 3Y2.
Find the mean and variance of C. (Round your answers to two decimal places.)