given that x={0,1}, y={0,1}, and that p(0,0)=p(1,1)=a/2 and p(0,1)=p(1,0)=(1-a)/2,why is it that the joint entropy can never be zero?

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- May 3rd 2012, 02:25 PMalexandrabel90joint entropy
given that x={0,1}, y={0,1}, and that p(0,0)=p(1,1)=a/2 and p(0,1)=p(1,0)=(1-a)/2,why is it that the joint entropy can never be zero?

- May 3rd 2012, 03:17 PMjensRe: joint entropy
The joint entropy is:

where is the so-called binary entropy function, which goes to zero only for or . So your entropy expression can only go to zero for or .