Suppose that Y1 and Y2 are independent exponential random variables, each having pdf fY(y) ey , y 0 If Y Y1 Y2, it can be shown that fY1 Y2 (y) 2yey, y 0 Recall Case Study 4 2 4 What is the probability that the next three eruptions of Mauna Loa will be less than forty months apart ...

Suppose that Y1 and Y2 are independent exponential random variables, each having pdf fY(y) =ey , y

Question:

Suppose that Y1 and Y2 are independent exponential random variables, each having pdf fY(y) =λe−λy , y > 0. If Y = Y1 + Y2, it can be shown that
fY1 + Y2 (y) =λ2ye−λy, y > 0
Recall Case Study 4.2.4. What is the probability that the next three eruptions of Mauna Loa will be less than forty months apart?