Consider a system consisting of three components as pic- tured. The system will continue to function as long as the first component functions and either component 2 or com- ponent 3 functions. Let X, X, and X, denote the lifetimes of components 1, 2, and 3, respectively. Suppose the X's are independent of one another and each X has an exponential distribution with parameter A. 2 3

a. Let Y denote the system lifetime. Obtain the cumulative distribution function of Y and differentiate to obtain the pdf. [Hint: F(y) = P(Yy); express the event {Y y} in terms of unions and/or intersections of the three events (Xy}, {y}, and {X, y}.]

b. Compute the expected system lifetime.