Lloyd eats X pieces of pizza, where X is an integer-valued random variable that is equally likely to be any of the values 1 through 8, inclusive. He takes the extra pizza home to his family, but if he eats too much pizza, he buys an extra pizza to take home too. Let Y be the number of pieces that he takes home to his family. Then, if 1 ≤ X ≤ 4, he does not need to buy any more pizza, so Y = 8 - X is the leftover. On the other hand, if 5 ≤ X ≤ 8, then Y = 16 - X, because he buys a second pizza in this case.