Stochastic

# 12 suppose that in a poisson process with rate we

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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.

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