# PS1--Answers - Econ 141 Problem Set 1 Answers Fall 2007 1...

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Econ 141: Problem Set 1: Answers Fall 2007 1. You ask 1000 people in a neighborhood (the total population of the neighborhood) about their education and employment status. The responses can be divided up into the following four categories: Unemployed, Non-college grads : 42 people Employed, Non-college grads : 694 people Unemployed, College grads : 9 people Employed, College grads : 255 people You decide to deﬁne the random variable X as 0 if the person is not a college grad and 1 if the person is, and the random variable Y as 0 if the person is unemployed and 1 if employed. What is E[ X ]? E[ Y ]? What is E[ Y | X = 0]? E[ Y | X = 1]? Answer: E[ X ] = 0 * (42 + 694) / 1000 + 1 * (9 + 255) / 1000 = 263 / 1000 = . 263 E[ Y ] = 0 * (42 + 9) / 1000 + 1 * (694 + 255) / 1000 = 949 / 1000 = . 949 E[ Y | X = 0] = 0 * 42 / (42 + 694) + 1 * 694 / (42 + 694) = 694 / 736 = . 943 E[ Y | X = 1] = 0 * 9 / (9 + 255) + 1 * 255 / (9 + 255) = 255 / 264 = . 966 2. We think that stock prices react to expectations about the future regulatory environ-

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