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Unformatted text preview: arrival time of the vehicle is random, and not at all connected to the signal (in particular, the
traﬃc signal is isolated and not synchronized with other signals that the vehicle passes) then it 10 CHAPTER 1. FOUNDATIONS seems intuitively reasonable to assign probabilities to the colors that are proportional to their dwell
2
5
1
40
8
times. Hence, we declare that P {green} = 30 = 5 , P {yellow} = 75 = 15 , and P {red} = 75 = 15 .
75
Note that the three outcomes are not equally likely. Example 1.2.3 (Standard unitinterval probability space) Take Ω = {ω : 0 ≤ ω ≤ 1}.3 Imagine
an experiment in which the outcome ω is drawn from Ω with no preference towards any subset. In
particular, we want the set of events F to include intervals, and the probability of an interval [a, b]
with 0 ≤ a ≤ b ≤ 1 to be given by
P ( [a, b] ) = b − a. (1.2) Taking a = b, we see that singleton sets {a} are events, and these sets have probability zero. In
order for the event axioms to be true, open intervals (a, b) must also be events and P ( (a, b) ) = b − a.
Any open subset of Ω can be expressed as the union of...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Institute of Technology.
 Spring '08
 Zahrn
 The Land

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