Suppose that a random variable X has the Poisson distribution with unknown mean ( 0) Find a statistic (X) that will be an unbiased estimator of e If E (X) e, then Multiply both sides of this equation by e, expand the right side in a power series in , and then equate the coefficients of x on both sides of the equation for x 0, 1, 2, 5(x)e e x X 0

Question: Suppose that a random variable X has the Poisson distribution with unknown mean ( > 0). Find a statistic (X) that will be an

Suppose that a random variable X has the Poisson with unknown mean Î» (Î» > 0). Find a statistic Î´(X) that will be an unbiased estimator of eÎ». If E[Î´(X)] = eÎ», then

Multiply both sides of this equation by eÎ», expand the right side in a power series in Î», and then equate the coefficients of Î»x on both sides of the equation for x = 0, 1, 2, . . . .

5(x)e-* = e. x! X=0

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