As you walk into your econometrics exam, a friend bets you $10 that she will outscore you on the exam. Let ✗ be a random variable denoting your winnings. X can take the values 10, if you win teh bet, 0 if there is a score tie, or -10 if you lose. You know that the probability distribution for ✗ is denoted by f(x) and it depends on whether she studied for the exam or not. Let Y be the random variable that indicates if she studied, Y = 0 if she studied and Y = 1 if she did not study. The following table denotes the joint distribution of X and Y : Y=0 Y=1 f(x) X = -10 0.18 P1 P2 X = 0 0 P3 0.3 X = 10 P4 0.45 P5 f(y) P6 0.75 Probabilities P1, P2, P3, P4, P5, P6 are not displayed in the table. Answer the following items: (a) (b) (a) Compute the Probabilities P1, P2, P3, P4, P5, P6 of the table. (b) Compute the expectation E(X). Should you take the bet? (c) What is the probability distribution of your winnings if you know that she did not study, namely, P(X = −10|Y = 1), P(X = 0|Y = 1), P(X = 10|Y = 1)? (d) Find your expected winnings \textbf{given that} she did not study, namely E(X|Y = 1). (c) (d)

As you walk into your econometrics exam, a friend bets you $10 that she will outscore you on the exam. Let ✗ be a random variable denoting your winnings. X can take the values 10, if you win teh bet, 0 if there is a score tie, or -10 if you lose. You know that the probability distribution for ✗ is denoted by f(x) and it depends on whether she studied for the exam or not. Let Y be the random variable that indicates if she studied, Y = 0 if she studied and Y = 1 if she did not study. The following table denotes the joint distribution of X and Y : Y=0 Y=1 f(x) X = -10 0.18 P1 P2 X = 0 0 P3 0.3 X = 10 P4 0.45 P5 f(y) P6 0.75 Probabilities P1, P2, P3, P4, P5, P6 are not displayed in the table. Answer the following items: (a) (b) (a) Compute the Probabilities P1, P2, P3, P4, P5, P6 of the table. (b) Compute the expectation E(X). Should you take the bet? (c) What is the probability distribution of your winnings if you know that she did not study, namely, P(X = −10|Y = 1), P(X = 0|Y = 1), P(X = 10|Y = 1)? (d) Find your expected winnings \textbf{given that} she did not study, namely E(X|Y = 1). (c) (d)

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.3: Conditional Probability; Independent Events; Bayes' Theorem

Problem 27E: Another friend asks you to explain how to tell whether two events are dependent or independent. How...

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