Let X1, X2, and X3 represent the times necessary to perform three successive repair tasks at a certain service facility.

Suppose they are independent, normal rv’s with expected values 1, 2, and 3 and variances 2 1, 2 2, and 2 3, respectively.

a. If
2
3
60 and 2 1
2 2
2 3
15, calculate P(X1 X2 X3  200). What is P(150  X1 X2 X3  200)?

b. Using the is and is given in part (a), calculate P(55  X)

and P(58  X  62).

c. Using the is and is given in part (a), calculate P(10  X1  .5X2  .5X3  5).

d. If 1
40, 2
50, 3
60, 2 1
10, 2 2
12, and 2

3
14, calculate P(X1 X2 X3  160) and P(X1 X2  2 X3).