a certain market has both an express checkout line and a super-express checkout line. let x1 denote the number of customers in line at the express checkout at a particular time of day, and let x2 denote the number of customers in line at the superexpress checkout at the same time. suppose the joint pmf of x1 and x2 is as given in the accompanying table.

Because of the violent nature of the sport, professional american football players are at risk of suffering concussions (or brain injuries) during the violent collisions that occur between players during the game. violent collisions involving hits to the head are particularly risky. suppose the commissioner of the national football league (nfl) institutes a rule requiring players to wear a new, lighter helmet that is designed to reduce head trauma during collisions between players on the field. while the new helmets the probability of a concussion resulting from each individual collision, at the same time the new helmets could also give football players an incentive to play more , which could potentially the amount of violent collisions and thus the number of concussions suffered by nfl players, all else equal.