Problem 7. It's Saturday night, and you're in your friend Zach's mom's basement, playing Dungeons and Dragons. In the game, your character rounds a corner in a subterranean maze, only to find a hideous slime monster. You must roll a large number on your dice to defeat the monster! You roll two (independent) 20-sided dice. Let X be the maximum of the two numbers and let Y be the minimum of the two numbers on the dice. 1 (a) You have taken the slime monster by surprise! You can use the larger of your two dice rolls. Find the probability mass function and cumulative distribution function of X. Hint: you may find it a little easier to start with the cumulative distribution function, and work from there to deduce the probability mass function. (b) The monster takes you by surprise! You must use the smaller of the two dice rolls. Find the probability mass function of Y