econ483midterm2009sol

econ483midterm2009sol - Econ 483 Midterm Spring 2009...

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Unformatted text preview: Econ 483 Midterm , Spring 2009, 08:30&10:10 You have 100 minutes. Total score is 80. Points are indicated in the [square brackets]. Questions that need to be answered are written in bold . [30 points] 2. Consider three random variables X , U , and Y . The &rst random variable X has a Uniform [0 ; 2] (the probability density function given by p ( x ) = 0 : 5 for & x & 2 and p ( x ) = 0 otherwise). The second random variable U has a N & &;¡ 2 ¡ where & = 0 and ¡ = 6 (with the probability density function given by 1 & p 2 ¡ exp & : 5( u & ¢ ) 2 =& 2 ). Suppose that X and U are independent. Finally, Y is a random variable determined by Y = ¢ + ¢ 1 X + U , where ¢ = 2 : 8 , ¢ 1 = 4 : 2 . [8] (1) Suppose that we estimate a linear model given by y i = £ + £ 1 x i + u i using the least squares method. (That is we &nd b = b £ and b 1 = b £ 1 that minimize Q n ( b ;b 1 ) = P n i =1 ( y i ¡ b ¡ b 1 x i ) 2 .) The slope parameter estimator based on the size n sample is given by b £...
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