Imagine the following game of chance. There are four dollar bills on the table. Your roll a fair die repeatedly. Every time you fail to get a six, one dollar bill is removed. When you get your first six, you get to take the money that remains on the table. If the money runs out before you get a six, you've lost and the game is over. Let X be the amount of your reward. Find the range and the probability mass function of X. Check that the p.m.f. you give adds up to 1.