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Econ 210 Spring 2009 Problem Set 2 - Solutions

Econ 210 Spring 2009 Problem Set 2 - Solutions - Econ 210...

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Econ 210 Spring Quarter 2009 Problem Set 2 - Solutions Solve the following problem. Show your work 1. TRUE/FALSE a. The median is a probability-weighted average of all possible realizations of a random variable FALSE. That is the definition of the mean (expected value) b. The probability of a particular realization of a continuous random variable is positive FALSE. Since there are an infinite number of realizations of a continuous random variable the probability of a particular realization is zero (1 over infinity). Hence, we can only ask questions about the probability that the random variable falls within an interval or is greater/smaller than a particular value. c. 1 1 N N i i i i i i a x a x = = = FALSE. See handout (or try with numbers). The thing to notice here is that the “a” has a subscript and thus varies from realization to realization. d. Let X be a (discrete) random variable with a total of N possible realization and let p(x) be its probability function, then ( 29 1 1 N i i p x = = TRUE. Taken over all possible realizations the probabilities have to sum to 1.
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