The maximum entropy distribution for a random variable x, Ask an Expert

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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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