A company has two electric generators. The time until failure for each generator follows an exponential distribution with mean 10. The company will begin using the second generator immediately after the first one fails.

Calculate the variance of the total time that the generators produce electricity.

• 10
• 20
• 50
• 100
• 200

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.

Solution: E

Let [math]X [/math] and [math]Y[/math] denote the times that the generators can operate. Now the variance of an exponential random variable is the square of the mean, so each generator has a variance of 100. Because they are independent, the variance of the sum is 200.

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.