Question: Let X n have the beta distribution with shape parameters n and 3, where n is any positive real number. a) Show that the distribution

LetXn have the beta distribution with shape parameters n and 3, where n is any positive real number. a) Show that the distribution of Xn belongs to an exponential family. b) Use a moment formula for exponential families to calculate E[logXn]. You may express your answer in terms of the digamma function, [t]:=dtdlog[t]. c) Use the previous result to evaluate the (improper) definite integral R01log[x]xn1(1x)2dx.

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