Let y 1 be the mean of a random sample of n 1 observations from a Poisson

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Let y̅1 be the mean of a random sample of n1 observations from a Poisson distribution with mean λ1, and let y̅2 be the mean of a random sample of n2 observations from a Poisson distribution with mean λ2. Assume the samples are independent.
a. Show that (y̅1 - y̅2) is an unbiased estimator of (λ1 - λ2).
b. Find V(y̅1 - y̅2). How could you estimate this variance?
c. Construct a large-sample (1 - α)100% confidence interval for (y̅1 - y̅2). Consider

as a pivotal statistic.

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Statistics For Engineering And The Sciences

ISBN: 9781498728850

6th Edition

Authors: William M. Mendenhall, Terry L. Sincich

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