Consider N independent random variables having identical binomial distributions with the parameters θ and n = 3. If no of them take on the value 0, n1 take on the value 1, n2 take on the value 2, and n3 take on the value 3, use the method of moments to find a formula for estimating θ.
Answer to relevant QuestionsUse the method of maximum likelihood to rework Exercise 10.53. In exercise Given a random sample of size n from a Poisson population, use the method of moments to obtain an estimator for the parameter λ. If X1, X2, . . . , Xn constitute a random sample of size n from a geometric population, find formulas for estimating its parameter α by using (a) The method of moments; (b) The method of maximum likelihood. Show that X + 1 / n + 2 is a biased estimator of the binomial parameter θ. Is this estimator asymptotically unbiased? 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 ...With reference to Example 10.4, find an unbiased estimator of β based on the smallest sample value (that is, on the first order statistic, Y1). Example 10.4 If X1, X2, . . . , Xn constitute a random sample from a uniform ...
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