Question: Let X, X, ..., X be a random sample from a population X with a pdf given by f(x) = ) = {1, if

Let X, X, ..., X be a random sample from a population X with a pdf given by f(x) = ) = {1, if a x b otherwise where a and b are two unknown real numbers satisfying a < b. i) Determine k (in terms of a and b); ii) Find the method of moments estimators (MME) for a and b respectively; iii) Given the observed sample 3, 2, 4, 3, 5, 6, 1, 4, find the moment estimates for a and b respectively.

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