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Unformatted text preview: r (Yi ) + (EYi )2 = EYi2 .
For a concrete example of the use of Theorem 2.10 consider
Example 2.3. Suppose that the number of customers at a liquor store in a
day has a Poisson distribution with mean 81 and that each customer spends an
average of $8 with a standard deviation of $6. It follows from (i) in Theorem
2.10 that the mean revenue for the day is 81 · $8 = $648. Using (iii), we see
that the variance of the total revenue is
81 · ($6)2 + ($8)2 = 8100 Taking square roots we see that the standard deviation of the revenue is $90
compared with a mean of $648. 88 CHAPTER 2. POISSON PROCESSES 2.4
2.4.1 Transformations
Thinning In the previous section, we added up the Yi ’s associated with the arrivals in our
Poisson process to see how many customers, etc., we had accumulated by time
t. In this section we will use the Yi to split one Poisson process into several.
Let Nj (t) be the number of i N (t) with Yi = j . In Example 2.1, where Yi is
the number of people in the ith car, Nj (t) will be the number of c...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell.
 Spring '10
 DURRETT
 The Land

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