Let y 1 be the mean of a random sample of n 1 observations from a Poisson distribution with mean 1 , and let y 2 be the mean of a random sample of n 2 observations from a Poisson distribution with mean 2 Assume the samples are independent a Show that (y 1 y 2 ) is an unbiased estimator of ( 1 2 ) b...

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

Question:

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