1) Suppose you have a standard deck of 52 cards. We will treat aces as a one. There are 4 suits. Each suit contains cards 1-10 and 3 face cards (Jack, Queen, King). Assign each face card a value of ten. (Every time a card is drawn it is replaced and the deck reshuffled.) We also have a 10 sided die with sides numbered 1-10. Lastly we have a coin with a 1 on one side and a 2 on the other. A) If you were to randomly draw a card, roll the die, and flip the coin. What is the expected value of each? B) Suppose that we form a data set using 50 card draws and 50 coin flips. We call our variables c and f. Which is likely larger Var(c) or Var(f)? Explain your answer. C) Suppose we reassign values to the face cards as 11, 12, and 13 for the Jack, Queen, and King. Would this increase, decrease, or have no effect on Var(c)? Explain D) Suppose a casino starts a game where the contestant places a bet, then pullsa card and rolls the die. If the value of the card and die is greater than x, the contestant wins. What is the minimum value x that the casino must set to make a profit? (Assume the casino has no other costs besides the payout.) 2) Using the 2010 National Survey of College Graduates, the average salary for a person who majored in Sociology or Anthropology is $49,370; while the average person whose major is best categorized as Computer and Mathematical Sciences earned an income of $68,120.75. Is this information sufficient to say that majoring in math causes a person to earn a higher income? Explain