1. Let X = (X, X,..., X) be a random sample from a discrete uniform distribution...

  

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1. Let X = (X₁, X₂,..., X) be a random sample from a discrete uniform distribution with support S = {1,2,...,0}, that is, with pmf f(x;0) = (1/0)1¸(x). (a) Show that the statistic ☎ = ((n+1)/k)X() is an unbiased estimator for for any k =1,2,...,n, where X is the kth order statistic. (b) Find the maximum likelihood estimators for and for the function g(0) =a +a0+ a₂0², where a are known constants. 1. Let X = (X₁, X₂,..., X) be a random sample from a discrete uniform distribution with support S = {1,2,...,0}, that is, with pmf f(x;0) = (1/0)1¸(x). (a) Show that the statistic ☎ = ((n+1)/k)X() is an unbiased estimator for for any k =1,2,...,n, where X is the kth order statistic. (b) Find the maximum likelihood estimators for and for the function g(0) =a +a0+ a₂0², where a are known constants.

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