The length of life Y for fuses of a certain type is modeled by the exponential distribution, with f (y) = (1/3)ey/3, y > 0, 0, elsewhere. (The measurements are in hundreds of hours.) a If two such fuses have independent lengths of life Y1 and Y2, find the joint probability density function for Y1 and Y2. b One fuse in part (a) is in a primary system, and the other is in a backup system that comes into use only if the primary system fails. The total effective length of life of the two fuses is then Y1 + Y2. Find P(Y1 + Y2 1).

Chapter 17 Multiple Regression Example: In the regression example from Chapter 15 notes we tried to predict the response variable weekly fuel consumption (FUEL) on the basis of predictor variable ‘average hourly temperature’ (TEMP) during the week. We saw a tendency for the FUEL to decrease in a straight-line fashion as the temperatures increase. Fuel consumption units are in Mcf (millions of...