Discussion6

# Discussion6 - Discussion 6 Emily Mower Contents 1 Textbook...

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Unformatted text preview: Discussion 6 Emily Mower February 24, 2010 Contents 1 Textbook: 3.55 2 2 Textbook 2.112 4 3 Textbook 2.114 5 4 Textbook 2.116 6 5 Textbook 2.131 7 1 1 Textbook: 3.55 Given the joint density function: f ( x,y ) = ( 6- x- y 8 , < x < 2 , 2 < y < 4 , elsewhere Find P (1 < Y < 3 | X = 1) = ? Solution: Things to find: f ( y | x ) and f ( x ) First, f ( x ): f ( x ) = Z 4 2 6- x- y 8 d y = 1 8 " 6 y- xy- y 2 2 4 2 # = 1 8 (6- 2 x ) = 3- x 4 Now find f ( y | x ) f ( y | x ) = f ( x,y ) f ( x ) = 6- x- y 8 3- x 4 = 6- x- y 2(3- x ) 2 Finally, solve for P (1 < Y < 3 | X = 1) P (1 < Y < 3 | X = 1) = Z 3 1 f ( y | x = 1) d y = Z 3 2 6- x- y 2(3- x ) x =1 d y = Z 3 2 6- 1- y 2(3- 1) d y = Z 3 2 5- y 4 d y = 1 4 " 5 y- y 2 2 3 2 # P (1 < Y < 3 | X = 1) = 0 . 625 3 2 Textbook 2.112 The probabilities that a service station will pump gas into 0, 1, 2, 3, 4, or 5 or more cars during a certain 30-minute period are 0.03, 0.18, 0.24, 0.28, 0.10, and 0.17, respectively. Find the probability that in this 30-minute period:and 0....
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Discussion6 - Discussion 6 Emily Mower Contents 1 Textbook...

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