Two components operate in parallel in a device so the device

Two components operate in parallel in a device, so the device fails when and only when both components fail. The lifetimes, X1 and X2, of the respective components are independent and identically distributed with an exponential distribution with theta=2. The costs of operating the device is Z=2Y1+Y2, where Y1=Min(X1,X2) and Y2=Max(X1, X2). Compute E(Z).

Solution