Let X € Rª be a random vector with the probability density function f(X) = e(x) for some function O : R^ → R, and normalization constant C. Show that f(X) is the distribution that attains the maximum

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Let X = R¹ be a random vector with the probability density function f(X) = ¹⁄eº(X) for some function
O: R → R, and normalization constant C. Show that f(X) is the distribution that attains the maximum
entropy among all distributions g such that Ex~g[0(X)] = k for some k. Make sure to justify every step.
Transcribed Image Text:Let X = R¹ be a random vector with the probability density function f(X) = ¹⁄eº(X) for some function O: R → R, and normalization constant C. Show that f(X) is the distribution that attains the maximum entropy among all distributions g such that Ex~g[0(X)] = k for some k. Make sure to justify every step.
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