As you walk into your econometrics exam, a friend bets you \(\$ 20\) that she will outscore you on the exam. Let \(X\) be a random variable denoting your winnings. \(X\) can take the values 20, 0 [if there is a tie], or -20 . You know that the probability distribution for \(X, f(x)\), depends on whether she studied for the exam or not. Let \(Y=0\) if she studied and \(Y=1\) if she did not study. Consider the following joint distribution Table P. 11

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a. Fill in the missing elements (i)-(vi) in the table.

b. Compute \(E(X)\). Should you take the bet?

c. What is the probability distribution of your winnings if you know that she did not study?

d. Find your expected winnings given that she did not study.

e. Use the Law of Iterated Expectations to find \(E(X)\).

Transcribed Image Text:

TABLE P.11 Joint pdf for Exercise P.15 Y 0 1 f(x) -20 (i) 0 (ii) X 0 (iii) 0.15 0.25 20 0.10 (iv) (v) f(y) (vi) 0.60