Let p(y) denote the probability function associated with a Poisson random variable with
Chapter 3, Problem 3.142(choose chapter or problem)
Let p(y) denote the probability function associated with a Poisson random variable with mean . a Show that the ratio of successive probabilities satisfies p(y) p(y 1) = y , for y = 1, 2,.... b For which values of y is p(y) > p(y 1)? c Notice that the result in part (a) implies that Poisson probabilities increase for awhile as y increases and decrease thereafter. Show that p(y) maximized when y = the greatest integer less than or equal to .
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