extra problems_04_27_2010 - Q1 Suppose that E(u | x v x v E(u E(v 0 E xu E xv 0 Show that for some E(u | x v E(u | v v Q2 Let y 1 x1 x2 u1 y 2 x1 u2 2 2

# extra problems_04_27_2010 - Q1 Suppose that E(u | x v x v...

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Q1. Suppose that ( | , ) , ( ) ( ) 0 E u x v x v E u E v , ( ) ( ) 0 E xu E xv . Show that for some , ( | , ) ( | ) E u x v E u v v . Q2. Let 1 1 2 1 2 1 2 ( , ) ( ) y x x u y x u where 2 1 1 2 1 var( | , ) u x x and 2 2 1 2 var( | ) u x . Show that 2 2 1 2 . Q3. Let 1 2 y x u , where , , y x u are random variables, 1 and 2 are parameters, and ( ) 0 E u . Show that if 2 cov( , ) / var( ) x y x , then ( ) 0 E xu . Q4. Find the inverse of the following matrices: 2 0 3 0 6 2 3 2 4 A ; 0 1 4 1 2 3 1 2 1 B ; 3 2 1 1 6 4 1 0 2 3 0 0 1 0 0 0 C . Hint: 1 a b d b c d c a ad bc and use the rule for inverse of partitioned matrix. Q5. Answer the following questions. (a) Find 2 1 det 1 5 . (b) Find 2 1 1 5 rank . (c) Find 1 0 0 2 0 1 rank .