1. Suppose you have a standard deck of 52 cards. We will treat aces...

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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 fair die with sides numbered 1-6. 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 the we form a data set using 50 card draws and 50 coin flips. We call our variables c and f. Which is likely larger V ar(c) or V ar(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 pulls a 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. Suppose we take a sample of wages for 30 year olds with and without a bachelor’s degree. We find that those with a degree earn 95% more than those without a degree. Does this mean that college education causes increased wages?

x y
2 17
5 1
2 15

3. Answer the following questions using the data in the table above.
(a) Calculate x, y
(b) Which variable has a higher variance? Explain intuitively.
(c) Without doing the math, are x and y positively correlated, negatively correlated, or not correlated? How can you tell?

4. Use the attached data set to complete the following questions/tasks with STATA. The project description has some additional details on the data.
• How many observations are there in the data set?
• Name 3 categorical variables from the data set.
• What is the range of mothers education for the sample?
• What is the median mother’s education?
• How many students earned ”mostly a’s” in eighth grade?
• Compare the mean current income for those that did and did not experience hard times.
• What are some possible reasons that those that experienced hard times as a kid might have different incomes?
• Create a histogram of current incomes.

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