5) (3 points) The mutual information of two random variables \(x, y\) is
\(I(x, y) = H(x) + H(y) - H(x, y)\)
where \(H(x)\), \(H(y)\) are the entropies of \(x\) and \(y\) and \(H(x, y)\) is the joint entropy which is defined as
\(H(x, y) = - \sum_{x} \sum_{y} p(x, y) \log[p(x, y)].\)
Show that \(I(x, y) \ge 0\). Hint: It can be useful to use \(p(x, y) = p(x|y)p(y)\).
