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.

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Is a  vector quantity  that refers to "the rate at which an object changes its position." imagine a person moving rapidly - one step forward and one step back - always returning to the original starting position. while this might result in a frenzy of activity, it would result in a zero velocity. because the person always returns to the original position, the motion would never result in a change in position. since velocity is defined as the rate at which the position changes, this motion results in zero velocity. if a person in motion wishes to maximize their velocity, then that person must make every effort to maximize the amount that they are displaced from their original position. every step must go into moving that person further from where he or she started. for certain, the person should never change directions and begin to return to the starting position.