how does one show that H(Y l f(X) ) greater than or equal to H(YlX) where f(X) is any function of X?

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- May 3rd 2012, 03:08 PMalexandrabel90conditional entropy of function
how does one show that H(Y l f(X) ) greater than or equal to H(YlX) where f(X) is any function of X?

- May 3rd 2012, 03:33 PMjensRe: conditional entropy of function
$\displaystyle f(X)$ is a degraded observation of $\displaystyle X$, so we have that

$\displaystyle H(Y|f(X),X) = H(Y|X)$

Since conditioning reduces entropy,

$\displaystyle H(Y|f(X)) \geq H(Y|X)$