It's Saturday night, and you're in your friend Zach's mom's basement, playing Dungeons and Dragons. Your game character rounds a corner in a subterranean maze, only to find a hideous slime monster.

You must attack the monster by rolling large numbers on your 20-sided dice. If you take the slime monster by surprise, then the amount of damage you deal to the monster is the maximum of your two rolls, but if the monster takes you by surprise, the amount of damage is the minimum of the two rolls.

You roll two (independent) 20-sided dice. Let R1 and R2 be the two rolls. Let X = max(R1,R2) and Y=min(R1, R2). Find the probability mass functions of X and Y.

Hint: First check that P(X=k)=P(Xk)P(Xk1) for an integer-valued random variable X, and then apply this property to find the PMF of X.