Consider a parallel system of 3 components: the system functions as long as at least one of its components functions. Let Xi be the lifetime of the ith component, and assume that Xi, i = 1, 2, 3, are i.i.d. exponential random variables with rate ?.
1. Let Z1 represent the time until the first failure. Find E[Z1].
2. Let Z2 represent the time until the second failure. Find E[Z2 ? Z1].
3. Find the expected system lifetime.