Unformatted text preview: 8 and can be proved in a similar way.
Example 1.2.1 (Toss of a fair coin) Suppose the experiment is to ﬂip a coin to see if it shows
heads or tails. Using H for heads and T for tails, the experiment is modeled by the following choice
of Ω and P :
Ω = {H, T }
F = {{H }, {T }, {H, T }, ∅}
1
P {H } = P {T } = ,
P (Ω) = P {H, T } = 1,
P (∅) = 0.
2 Example 1.2.2 A particular experiment is to observe the color of a traﬃc signal at the time it is
approached by a vehicle. The sample space is Ω = {green, yellow, red} and we let any subset of Ω
be an event. What probability measure, P , should we choose? Since there are three colors, we could
declare them to be equally likely, and thus have probability 1/3 each. But here is an intuitively
more reasonable choice. Suppose when we examine the signal closely, we notice that the color of
the signal goes through cycles of duration 75 seconds. In each cycle the signal dwells on green for
30 seconds, then dwells on yellow for 5 seconds, then dwells on red for 40 seconds. Assuming that
the...
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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 Tech.
 Spring '08
 Zahrn
 The Land

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