quiz9solns - STA 4321/5325 Spring 2010 Quiz 9 April 16 Name...

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Unformatted text preview: STA 4321/5325 - Spring 2010 Quiz 9 - April 16 Name: There are five problems in this quiz. Each problem has exactly one correct answer. Problem 1 Let X and Y be independent random variables with E (X ) = 2, E (Y ) = 1, V (X ) = 16, and V (Y ) = 3. Then (a) E (X 2 Y 2 ) = 0 (b) E (X 2 Y 2 ) = 35 (c) E (X 2 Y 2 ) = 80 (d) We can not find E (X 2 Y 2 ) with given information. Solution: E (X 2 Y 2 ) = E (X 2 )E (Y 2 ) = V (X ) + (E (X ))2 16 + 22 = V (Y ) + (E (Y ))2 3 + 12 = 80 Hence, The correct answer is C. Problem 2 Let ρ be the correlation between two random variables X and Y . It is NOT true that (a) ρ is a unitless quantity (b) −1 ≤ ρ ≤ 1 (c) If ρ = 1, Y = aX + b where a > 0 (d) If ρ is close to −1, then linear relationship between X and Y is very weak. Solution: The correct answer is D. Problem 3 Let ρ be the correlation between two random variables X and Y . If X and Y is independent then ρ = 0. This statement is always (a) True (b) False Solution: If X and Y is independent then COV(X, Y ) = 0. Hence, the correct answer is A. 1 Problem 4 Let X and Y be two random variables with V (X ) = 100, V (Y ) = 100, and COV(X, Y ) = 30. Then (a) V (X + Y ) = 100 (b) V (X + Y ) = 230 (c) V (X + Y ) = 260 (d) V (X + Y ) = 140 Solution: V (X + Y ) = V (X ) + V (Y ) + 2COV(X, Y ) = 100 + 100 + 2(30) = 260 The correct answer is C. Problem 5 Let X and Y be two continuous random variables with joint probability density function, f (x, y ). Then the conditional expectation of X is given Y = y is defined as (a) E (X |Y = y ) = ∞ −∞ xfX |Y =y (x)dx (b) E (X |Y = y ) = ∞ −∞ xf (x, y )dx (c) E (X |Y = y ) = ∞ −∞ xfX (x)dx (d) E (X |Y = y ) = ∞ −∞ xfY (y )dy Solution: By definition, the correct answer is A. 2 ...
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This note was uploaded on 08/05/2011 for the course STA 4321 taught by Professor Staff during the Fall '08 term at University of Florida.

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quiz9solns - STA 4321/5325 Spring 2010 Quiz 9 April 16 Name...

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