Coin tosses: independence and sums

A fair coin is tossed three times. Let \(X\) be the number of heads on the first two tosses, \(Y\) the number of heads on the last two tosses.

1. Make a table showing the joint distribution of \(X\) and \(Y\).
2. Are \(X\) and \(Y\)  independent ?
3. Find the distribution of \(X+Y\) ?