Question

(21%) Consider the parallel circuit with probability as follows: 3. C1 with success prob p1 C2 with success prob p2 (a) 3%) Compute the probability p of sending data successfully through this circuit as a function of pı and p2 (b) (3%) If p1 p2 1, find the maximum ql and also the minimum q2 of p. Prove or reason that the maximum value qi of p and minimum value q2 of p you find are really the maximum and the minimum (c) (3%) Redo (b) with the restriction pl+p2 = 1 removed (d) (6%) Suppose we have 0.5 pl 0.9 and 0.6 < p2 0.8. Compute now the maximum q1 and minimum q2 of the probability p of sending data successfully through this circuit. Prove why your answer is correct (e) (6%) Generalize part (d) to have a pl band c p2 d (where obviously 0<a and 0 c) Compute the maximum q1 and minimum q2 +

Answer 1

Ancaer () The probalility ?ending this Circ is P CCi Cit ith suces datSuccess ess P C2 with success)-P(CI ith success AND P(CI ith su CC C2 with success Hence, P- Pl P2 A P2 B ae no hat Pt-1 axiu 91 , pi is o.4 then q1 PI 10.4 O. 2, P2 is o. them 12 -P2 -1-0.8 lecause 1- P O.4 o.8. P- o.4+0.8 and Jrarallel -1-11*92 1- 2 91 92 0.12 0 o 2 O.88 Hence, Magie qi- O 6 and Mniuo 92-