sample_questions_part_1

# sample_questions_part_1 - Econ 177 Sample Questions Part I...

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Econ 177 Sample Questions Part I In all the questions that follow you may assume each of the i = 1 ,...,n bidders’ values are drawn independently from the uniform distribution on [0,100], which is deﬁned as follows F ( v ) = Pr[˜ v i v ] = v 100 . 1. What is the probability that individual i ’s value draw is equal to 60, is less than 60, is less than or equal to 60? 2. Let ˜ v (1) denote the random variable for the highest of the n bidders’ use-value draws. (a) Compute F (1) ( · ) , the distribution of ˜ v (1) . (b) Compute f (1) ( · ) , the density function of ˜ v (1) . 3. Let ˜ v (2) denote the random variable for the second-highest of the n bidders’ use-value draws . (a) Compute F (2) ( · ) , the distribution of ˜ v (2) . (b) Compute f (2) ( · ) , the density function of ˜ v (2) . 4. Compute the expected value of ˜ v (1) . 5. Evaluate the following claim: In a SPA you should bid more than your value because you increase your probability of winning the auction and

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sample_questions_part_1 - Econ 177 Sample Questions Part I...

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