Question

(15 pts) You know that there is a problem in your car due to sounds you hear when driving. There can be only two sources for the problem 1) Brakes 2) Engine. You are estimating that the problem is due to brakes with probability 0.6, and it is due to engine with probability 0.4. Furthermore, if the problem is due to brakes or engine, the number of miles you can drive without any repair is exponentially distributed with mean 500 and 100 miles, respectively. a) What is the probability that the number of miles you can drive the car without any repair is larger than 200 miles.? b) What is the expected number of miles you can drive the car without any repair?

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Answer 1

det y be the number of miles it can delive Sed without repair them Y- = 0.6 Xot 0.4X2 I Brakes because wp = 0.6, it drives Xini Exe (soo) (problem ор 0.4, it drives X₂ ~ Exp (oo) Enquire Problem Need to find Q (42200) P(0.6%, +0:14 x2 2 200) = P(x, 2 200-04x3) 0:6 Kaos X,=0 S fxz(82) Exi(n) dridae X2=0 *,- 200-04X2 0.6 fiz (x2) fxo (n.) anidra .X20 ke=200-0-412 _Az Š S-M, } exp }dkidez exp Too soo N=0 soo .,-200-0.482 ob 2 Š exp } drudnia 100 Soooo -X, exp. Soo 1,=200-0442 0:6 hi exp lexe ni (500) dk, Soooo Soo Sou k, = 200-8:14 Kz NE 200-0.442 0.6 0.6

0.482 \ဝပ် 0.6 X Soo Senelitian deve los Sexp {1, 2} 2002 exploitations dxz -200 exp ܘܘܐ Serpentina +0.4H2 loo sobe} exp{z}} dxz Exp{ // } so exp {-2.672 } diz 100 exp{-} 3} 300 XI 2.6 ܘ ܘܪ 3 X exp 2.6 b) E(Y) E C 0.6X1+0.4x2) (0.6)x 500+ so +(0.4)*100 300t yo E(Y) = 34.0 Please give me an upvote.