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4 Suppose that the number of cars visiting New Paltz has Poisson distribution with a...

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4 Suppose that the number of cars visiting New Paltz has Poisson distribution with a parameter A 0 There are three types of cars diesel sedan and truck The probability of randomly chosen car is a diesel sedan or truck is P P2 and p3 with p P2 P3 1 and the event of each car being a certain type is independent of each other Let X Y Z be numbers of diesel cars sedans or trucks during one day a Suppose that there are n distinct items We want to divide n items into three groups group A B and C with a b and c elements with a b c n Show that the number of different grouping is c n a b c alxblxc b Show that a b c a b c P1P2P3 X a b c a b c 1

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