HW5 (Due 10/24)

Consider Teams A and B play against each other for the final of a volleyball tournament. The team who won 3 matches first win the tournament. Let \(X\) be the outcome of the game. For example, \(X\) can be AAA, BBB, AABA, ABAA. And let \(Y\) be the number of matches played, so \(Y\) can be 3,4, or 5. Please try to compute

1. \(H(X)\)

2. \(H(Y)\)

3. \(H(X|Y)\)

4. \(H(Y|X)\)

5. \(H(X,Y)\)

Let say we throw a dice twice and the outcomes are \(D_1\) and \(D_2\). And let \(S=D_1 + D_2\). Please compute

1. \(H(D_1|S=3)\)

2. \(I(D_1;D_2|S=3)\)

3. \(I(D_1;D_2|S)\)