Question

How can I prove that H(X,Y)=H(X) + H(Y|X)?

Answer 1

I understood up until the part that \[H(X,Y)= -\sum_{X}^{ }\sum_{Y}^{ }p(X,Y)\log(p(X,Y))\]

Answer 2

and then p(x,y)=p(X)p(Y|X) thus \[-\sum_{X}^{ }\sum_{Y}^{ } p(x,y)[ \log p(X) +\log p(Y|X)]\]