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The maximum entropy distribution for a random variable X for which G(X) and its expectation, E[G(X)], are speci?ed, was given in Eq (10.85) for discrete X, and Eq (10.89) for continuous X i.e., ( Ce-λG(xi ); for discrete Xf (x) = Ce-λG(x); for continous X
Determine f (x) completely (i.e., determine C and λ explicitly) under the following conditions:
(i) G(Xi ) = 0; i = 1, 2,. .., k, a discrete random variable for which nothing is known except its range;
(ii) G(X) = 0; a <>X b;
(iii) G(Xi ) = X; i = 1, 2,. . .; E[G(X)] = μ
(iv) G(X) = X;0 x ∞; E[G(X)] = μ
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You have been hired as a consultant by your local mayor to look at the various market structures. Your role is to provide analysis and answers to these important questions that will help the mayor understand the structures of many of the businesse..
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