P Set 3

P Set 3 - Problem Set 3 MGTECON 603 2009 1 MGTECON 603...

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Unformatted text preview: Problem Set 3, MGTECON 603, 2009 1 MGTECON 603, Econometrics I Jules H. van Binsbergen and Ying Xue Fall 2009 Stanford GSB PROBLEM SET 3 Due: Friday October 16 th in class 1. Let X and Y be independent standard normal rv’s and define a new rv Z by Z = braceleftbigg X if XY > − X if XY < (a) What is the distribution of Z ? (What is its name, etc.) (b) Show that the joint distribution of Z and Y is not bivariate normal. 2. Let X given Y = y have a normal distribution with mean y and variance one, and let the marginal distribution of Y be normal with mean μ Y and variance σ 2 Y . What is the distribution of Y given X = x ? 3. Let X 1 , X 2 , ... , X N given Y = y have independent normal distributions with mean y and variance one, and let the marginal distribution of Y be normal with mean μ Y and variance σ 2 Y . What is the distribution of Y given X 1 ,X 2 ,...,X N ? 4. Let X given Y have a binomial distribution with parameters n and y , and let the marginal distribution of Y be Beta with parameters...
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P Set 3 - Problem Set 3 MGTECON 603 2009 1 MGTECON 603...

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