Chapter 7: Problem 4
Let \(X_{1}, X_{2}, \ldots, X_{n}\) be a random sample from a Poisson distribution with parameter \(\theta>0\) (a) Find the MVUE of \(P(X \leq 1)=(1+\theta) e^{-\theta}\). Hint: \(\quad\) Let \(u\left(x_{1}\right)=1, x_{1} \leq 1\), zero elsewhere, and find \(E\left[u\left(X_{1}\right) \mid Y=y\right]\), where \(Y=\sum_{1}^{n} X_{i}\). (b) Express the MVUE as a function of the mle. (c) Determine the asymptotic distribution of the mle.
Short Answer
Step by step solution
Key Concepts
These are the key concepts you need to understand to accurately answer the question.