Using the fact that a Poisson process results when the times between successive events are independent and identically distributed exponential random variables, show that P X n F2 2n (x) when X is a Poisson random variable with mean x 2 and F2 2n is the chi square distribution function with 2n degrees of freedom (Hint Use the results of Section 14 3 2 )

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Question: Using the fact that a Poisson process results when the times between successive events are independent and identically distributed exponential random variables, show that P{X

Using the fact that a Poisson process results when the times between successive events are independent and identically distributed exponential random variables, show that P{X ≥ n} = Fχ2 2n

(x)

when X is a Poisson random variable with mean x/2 and Fχ2 2n is the chi-square distribution function with 2n degrees of freedom. (Hint : Use the results of Section 14.3.2.)

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