SOLUTION: On the way to work a person passes through three intersections monitored by traffic lights. The location and operation of these traffic lights is such that, to all intents and purp

Question 770669: On the way to work a person passes through three intersections monitored by traffic lights. The location and operation of these traffic lights is such that, to all intents and purposes, they appear to operate independently to a person travelling from one to another. The probability of a red light is 0.4, 0.8, and 0.5 respectively for each of the traffic lights.

(a) Find the probability function of X, the number of red lights the person encounters in a single trip.
(b) Compute the mean of X.
(c) Assume that the waiting time for each red light is two minutes. What is the mean waiting
time in one trip?
Answer by oscargut(2103) (Show Source): You can put this solution on YOUR website!
On the way to work a person passes through three intersections monitored by traffic lights. The location and operation of these traffic lights is such that, to all intents and purposes, they appear to operate independently to a person travelling from one to another. The probability of a red light is 0.4, 0.8, and 0.5 respectively for each of the traffic lights.

(a) Find the probability function of X, the number of red lights the person encounters in a single trip.
(b) Compute the mean of X.
(c) Assume that the waiting time for each red light is two minutes. What is the mean waiting
time in one trip?
Answer:

a)
P(X=0) = 0.6*0.2*0.5 = 0.06
P(X=1) = 0.4*0.2*0.5 + 0.6*0.8*0.5 + 0.6*0.2*0.5 = 0.04+0.24+0.06 = 0.34
P(X=2) = 0.4*0.8*0.5 + 0.4*0.2*0.5 + 0.6*0.8*0.5 = 0.16+0.04+0.24 = 0.44
P(X=3) = 0.4*0.8*0.5 = 0.16
b)
E(X) = 0(0.06)+1(0.34)+2(0.44)+3(0.16) =0.34+0.88+0.48 = 1.7

c) 2*1.7 = 3.4

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