Consider three lightbulbs each of which has a lifetime that is an independent exponential random variable with parameter λ=1. The variance of the time until all three burn out is:

Question

=

Recall that the variance of an exponential with parameter λ is 1/λ2.

Answer 1

1/3 ?

Answer 2

11/6 why it is wrong? could anyone explain this?

Answer 3

1/9 +1/4 + 1 = 1.361111