Suppose that X1,.., Xn is a random sample from the Poisson distribution with parameter 1 > 0. Let X and S? denote the sample mean and sample variance, respectively. (1) Show that (X,S²) is sufficient but not complete. (2) Prove the rather remarkable identity E(S2|X) = X.
Suppose that X1,.., Xn is a random sample from the Poisson distribution with parameter 1 > 0. Let X and S? denote the sample mean and sample variance, respectively. (1) Show that (X,S²) is sufficient but not complete. (2) Prove the rather remarkable identity E(S2|X) = X.
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.CR: Chapter 13 Review
Problem 43CR
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