Poor serfs are bringing eggs to the queen and receive gold coins in exchange. Each egg is worth ten gold coins. However, if a serf brings eggs worth more than 6,700 gold coins in total, the queen will pay 1,600 gold coins less for them to make sure landowners won't get as rich as Her Majesty. If they bring eggs worth from 5,000 to 6,700 gold coins (inclusive), the pay is reduced only by "only" 1,000 gold coins.
A farmer is breeding hens that lay from 0 to 1,000 eggs per week (uniformly randomly distributed), which he brings to the queen each Sunday. What is the average (expected) amount of gold coins he earns per week?