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2010_EC507_HW3

# 2010_EC507_HW3 - EC507Statistics for Economists Fall Spring...

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EC507—Statistics for Economists Fall Spring 2010 Problem Set 3 1. Suppose a grasshopper is sitting in the middle of a long narrow tiled hallway. It moves along by jumping distances of one tile to the right or left down the length of the hallway. With probability p (0 p 1), the grasshopper will jump one unit to the left, and with probability is 1-p that the grasshopper will jump one unit to the right. How far away do you expect the grasshopper to be after n jumps relative to where it started? (That is, find the expected value of the distance away from the grasshopper’s starting point.)

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2. Suppose that a person’s IQ is uniformly distributed between the IQ levels of his/her parents. Let parents’ IQ be a and b such that a < b. Find the mean and variance of children’s IQ.
3. Let X be a random variable with . 4 ) ( , 2 ) ( = = X V X E Let Y be a random variable with . 2 ) ( , 1 ) ( = = Y V Y E a. Find ). 2 3 ( Y X E + b. Find ) ( Y X V , assuming X and Y are independent.

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c. Find ) 2 3 ( Y X V + , assuming X and Y are independent.
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2010_EC507_HW3 - EC507Statistics for Economists Fall Spring...

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