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3a. On a certain aircraft, the main control circuit on an autopilot fails with probability p. A redundant backup eircuit fails independently with probability q. The aircraft can fly if at least one of the circuits is functioning. Find the probability that the aircraft cannot fly. 4 pt. b. Let X and Y be the random variables with respective pmfs shown in the side figure. Compute var(X), var(Y). 23 pt. 3 pt. c. | At Problem 3-b, find the PMF of the DRV Z--X+Y.

math   Statistics-And-Probability   
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Soluction (3) Fom ven dda Cicu on an aiop P. TC let Co side, en (br let x and y be- Yoobm arable url, edpechve Pmfs sloon in-祐 sidega (given in guer.on)· や where , EX、 S,P(x:1) F (x): x P(x) 6 33 6、13 where 구(2)-1 6+2妥:父+y: -y,-3 ,-2,1,0,1, 2, 3, y, 3 36qPCx-o) P (y-o)十Р (х -z) P (yen).tr(x-:) P(yr-)-t Pix-- ) 3

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