24If9and we wanted to determine(8)P X, we would go to the appropriate column and look downto8xand finalize our answer:(8)(8).4557P X Example:Determine(6)P Xfor a Poisson random variable with9(6)(6)(5).2068.1157.0909P X .
Exercise:Determine(7)PXfor a Poisson random variable with4Theorem:If the number of events in a time interval t follows a Poisson distribution with mean, thenthe number of events in time periodk tfollows a Poisson distribution with meankThis is quite a common sense theorem. If arrivals occur at a rate of 10 per hour, we could also say 20 per2-hour period, 5 per half hour, 2.5 per 15-minute period etc.Suppose thatXcounts the number of arrivals in a 20 minute period andPoi(8)X. (ReadXdistributed). Thus, the rate is 8 per 20-minute time period. Suppose that we want to determineprobability questions over a 25-minute period. What would our newbe?..is,
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Exercise:Determine(9)PY.