Question

Problem 7: [8 points] The length of time to failure (in hundred of hours) for a transistor is a random variable Y with c.d.f. given by F(y) {: 1 - exp{-yº}, if y20, 0, elsewhere. (a) Find the p.d.f f(y) of Y and show that it is indeed a valid p.d.f [2] (b) Find the 30th percentile of Y and interpret it [2]. (c) Find E(Y) and V(Y) [2] (d) Find the probability that the transistor operates for at least 200 hours. [1] (e) Find P(100 <Y <200). [1]

Answer 1

ANSWER: Criven that y is nov. with codif. -|-exp(-32) if yao Fly) elsewhere af Find pdef of y f)= df) db 2y exp(-32) if you else where b) 30th precentile oty is given by -T3o 0 :3 = finy day Too 0.3 = . 2y exp(-42) day 2 _530 O-3 =-e *] =1-03 => e - Rz? In (0.7) = 720=f- ln (0.7) Tho=0.5972 As SJ EV) ad? ده ردا 4 5 こ y ay y f (y) dy - e dy Ely)=2 va ent(o) E (²) 0.9862 {ent com sert (1) = 0 2