# Question

After referring to Example 10.4, is the nth order statistic, Yn, a sufficient estimator of the parameter β?

## Answer to relevant Questions

If X1 and X2 constitute a random sample of size n = 2 from a Poisson population, show that the mean of the sample is a sufficient estimator of the parameter λ. Given a random sample of size n from a beta population with β = 1, use the method of moments to find a formula for estimating the parameter α. X1, X2, . . . , Xn constitute a random sample of size n from a gamma population with α = 2, use the method of maximum likelihood to find a formula for estimating β. Given a random sample of size n from a gamma population with the known parameter α, find the maximum likelihood estimator for (a) β; (b) t = (2β – 1) 2. If X has a Poisson distribution and the prior distribution of its parameter Λ(capital Greek lambda) is a gamma distribution with the parameters α and β, show that (a) The posterior distribution of given X = x is a gamma ...Post your question

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