Chapter 4: Problem 12
. Let \(X_{1}, X_{2}, \ldots, X_{n}\) be a random sample from a Poisson distribution with mean \(\mu .\) Thus \(Y=\sum_{i=1}^{n} X_{i}\) has a Poisson distribution with mean \(n \mu .\) Moreover, \(\bar{X}=Y / n\) is approximately \(N(\mu, \mu / n)\) for large \(n .\) Show that \(u(Y / n)=\sqrt{Y / n}\) is a function of \(Y / n\) whose variance is essentially free of \(\mu .\)
Short Answer
Step by step solution
Key Concepts
These are the key concepts you need to understand to accurately answer the question.