Let X1, X2, and X3 represent the times necessary to performthree successive repair tasks at a service facility. Suppose theyare normal random variables with means of 50 minutes, 60 minutes,and 40 minutes, respectively. The standard deviations are 15minutes, 20 minutes, and 10 minutes, respectively.
a) Suppose X1, X2, and X3 are independent. All three repairsmust be completed on a given object. What is the mean and varianceof the total repair time for this object?
b) Suppose X1, X2, and X3 are independent. All three repairsmust be completed on a given object. Find the probability that thetotal repair time is less than 180 minutes.
c) Suppose that X1, X2, and X3 are dependent so that thecovariance between X1 and X2 is -150, between X1 and X3 is 60, andbetween X2 and X3 is -45. If all three repairs must be completed ona given object, what is the mean and variance of the total repairtime for this object?
