Start with $1500 in the bottom right corner on the Sorting Hat Square

Roll two dice and move in a clockwise direction the number of squares indicated by thesumof the dice.

If your dice add to 2, move the to Ministry of Magic square*. Take a "Potions" card and pay/receive the specified amount.

(* otherwise known to Muggles as "Community Chest")

If your dice add to 4 then move to Fluffy's square, be attached, and pay the bank $200.

If your dice add to 7, move to the "Charms" square* and take a card, and pay / receive the specified amount.

(* otherwise known to Muggles as "Chance")

Potions

If you land on the Ministry of Magic square, you draw one of the following 4 cards, shuffled into random order:

• Professor Slughorn gives you Felix Felicis to reward your exceptional potions work.Collect $100.
• You are appointed Minister of Magic.Pay each other player $50.(You are playing with 3 others.)
• Escape from Azkaban.No cash payment or receipt.
• Poor tax.Pay $20.

Charms

If you land on the Charms square, you draw one of the following 4 cards, shuffled into random order:

• Whomping Willow whomped you senseless. Madam Pomfrey fixes you with Skele-Gro.Pay doctor's fees of $50.
• You won second prize in the Triwizard Tournament.Collect $150.
• Your vanishing spell goes wrong. Go back 3 places and...pay the consequences!
• Go directly to Azkaban. Do not pass Go, do not collect $200.No cash payment or receipt.

Questions:

1. LetMbe a random variable denoting the cash value (positive = income, negative = payment) from landing on the Ministry of Magic square. CalculateE(M) and sd(M).
2. LetCbe a random variable denoting the cash value (positive = income, negative = payment) from landing on the Charms square. CalculateE(C) and sd(C).