Consider a system consisting of three components as pictured. the system will continue to function as long as the first component functions and cither component 2 or component 3 functions. let x1, x2, and x3 denote the lifetimes of components 1, 2, and 3, respectively. suppose the x, s are independent of one another and each x1 has an exponential distribution with parameter. let y denote the system lifetime. obtain the cumulative distribution function of y and differentiate to obtain the pdf. [hint: f(y) = p(y y): express the event [ y y] in terms of unions and/or intersections of the three events {x1 y}, {x2 y}, and {x3 y}.] compute the expected system lifetime.