Chapter 7: Problem 8
Let \(X\) have the pmf \(p(x ; \theta)=\frac{1}{2}\left(\begin{array}{l}n \\\ x\end{array}\right) \theta^{|x|}(1-\theta)^{n-|x|}\), for \(x=\pm 1, \pm 2, \ldots, \pm n\), \(p(0, \theta)=(1-\theta)^{n}\), and zero elsewhere, where \(0<\theta<1\) (a) Show that this family \(\\{p(x ; \theta): 0<\theta<1\\}\) is not complete. (b) Let \(Y=|X| .\) Show that \(Y\) is a complete and sufficient statistic for \(\theta\).
Short Answer
Step by step solution
Key Concepts
These are the key concepts you need to understand to accurately answer the question.