Solution Found!
Answer: Let Y1, Y2, . . . , Yn denote a random sample from
Chapter 9, Problem 112SE(choose chapter or problem)
Let denote a random sample from a Poisson distribution with mean \(\lambda\) and define
\(W_{n}=\frac{\bar{Y}-\lambda}{\sqrt{\bar{Y} / n}}\)
a. Show that the distribution of \(W_{n}\) converges to a standard normal distribution.
b. Use \(W_{n}\) and the result in part (a) to derive the formula for an approximate \(95 \%\) confidence interval for \(\lambda\).
Equation Transcription:
Text Transcription:
Y1, Y2,...,Yn
\lambda
W_n=\frac\bar Y-\lambda \sqrt\bar Y / n
W_n
W_n
95%
\lambda
Questions & Answers
QUESTION:
Let denote a random sample from a Poisson distribution with mean \(\lambda\) and define
\(W_{n}=\frac{\bar{Y}-\lambda}{\sqrt{\bar{Y} / n}}\)
a. Show that the distribution of \(W_{n}\) converges to a standard normal distribution.
b. Use \(W_{n}\) and the result in part (a) to derive the formula for an approximate \(95 \%\) confidence interval for \(\lambda\).
Equation Transcription:
Text Transcription:
Y1, Y2,...,Yn
\lambda
W_n=\frac\bar Y-\lambda \sqrt\bar Y / n
W_n
W_n
95%
\lambda
ANSWER:
Step 1 of 3
Given data:
The equation for Poisson distribution is:
