hw03_sol - Homework 3 September 17, 2007 Problem 1. Let A =...

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Unformatted text preview: Homework 3 September 17, 2007 Problem 1. Let A = A student passes the course P ( A ) = 0 . 7 and P ( x = 1 . 0) = P ( A C ) = 0 . 3 , P ( x = 2 . 0) = P ( x = 2 . ∩ A ) = P ( x = 2 . | A ) × P ( A ) = 0 . 7 × . 5 = 0 . 35 P ( x = 3 . 0) = P ( x = 3 . ∩ A ) = P ( x = 3 . | A ) × P ( A ) = 0 . 7 × . 3 = 0 . 21 P ( x = 4 . 0) = P ( x = 4 . ∩ A ) = P ( x = 4 . | A ) × P ( A ) = 0 . 7 × . 2 = 0 . 14 Thus X is discrete. Problem 2. (a)For all f ( x ) , R ∞-∞ f ( x ) dx = 1 . Thus, R ∞-∞ f ( x ) dx = R-∞ f ( x ) dx + R ∞ f ( x ) dx = 0+ R ∞ ce- 3 x dx =- 1 3 ce- 3 x | ∞ = 1 3 c = 1 ⇒ c = 3 . (b) P [ x > 3] = R ∞ 3 3 e- 3 x =- e- 3 x | ∞ 3 = 0- (- e- 9 ) = e- 9 Problem 3. Let A = ( x,y ) is within 1 2 a unit of distance away from at least one vertex. Since ( X,Y ) is uniformly distributed, thus P ( A ) = S A S 4 , where S A is the area of the region A and S 4 is the area of the triangle.....
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This note was uploaded on 11/12/2008 for the course ORIE 360 taught by Professor Ehrlichman during the Fall '07 term at Cornell.

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hw03_sol - Homework 3 September 17, 2007 Problem 1. Let A =...

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