ANTest2-07 - Answers for Test # 2; March 1, 2007 1. (10) In...

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Unformatted text preview: Answers for Test # 2; March 1, 2007 1. (10) In a Taylor series expansion for f ( x,y ) = e x cos( y ) , find the coefficient for ( x- 0) 3 ( y- π ) 2 . Answer: This coefficient will be 1 3!2! ∂ 5 f (0 ,π ) ∂x 3 ∂y 2 . By differentiating, we have that ∂ 5 f ( x,y ) ∂x 3 ∂y 2 =- e x cos( y ) , so ∂ 5 f (0 ,π ) ∂x 3 ∂y 2 =- e cos( π ) = 1 . Therefore the coefficient is 1 3!2! . 2. (15) For X ∼ N (1 , 4) , find the pdf for Z = X 2 . Answer: P (0 ≤ Z ≤ t ) = P (0 ≤ X 2 ≤ t ) = P (- √ t ≤ X ≤ √ t ) = 1 2 √ 2 π R √ t- √ t e- 1 2 ( x- 1 2 ) 2 dx. Therefore, differentiating with respect to t yields f ( t ) = 1 2 √ 2 π [ 1 2 t- (1 / 2) e- 1 2 ( t 1 / 2- 1 2 ) 2 + 1 2 t- (1 / 2) e- 1 2 (- t 1 / 2- 1 2 ) 2 ] . 3. a. (3) State the Efficient Market Hypothesis. Answer: All information from the past already is incorporated into the price, all current informa- tion already is incorporated into the price. b. (2) Give an example where the EMH holds, and where it does not. Answer: You can get this from the notes. 4.(15) In playing a game where a die is rolled, if a 5 or 6 occur, I win $ 600; if any other number occurs, I lose $ 300. Find the likelihood that, after playing the game 121 times, a person will go300....
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This note was uploaded on 09/12/2009 for the course MATH 45240 taught by Professor Saari during the Spring '09 term at UC Irvine.

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ANTest2-07 - Answers for Test # 2; March 1, 2007 1. (10) In...

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