HW 22 Answers (8.1)

HW 22 Answers (8.1) - Math331, Spring 2008 Instructor:...

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Unformatted text preview: Math331, Spring 2008 Instructor: David Anderson Section 8.1 Homework Answers Homework: pgs. 325 - 326, #s 1, 2, 3, 4, 5, 7. 1. We have that p ( x, y ) = braceleftBigg k parenleftBig x y parenrightBig if x = 1 , 2 , y = 1 , 2 else . (a) We must have 1 = 2 summationdisplay x =1 2 summationdisplay y =1 kx/y = k 2 summationdisplay x =1 x (1 + 1 / 2) = k (3 / 2) * 3 = (9 / 2) k. Therefore, k = 2 / 9. (b) The marginal probability mass functions are p X ( x ) = 2 summationdisplay y =1 p ( x, y ) = (2 / 9) 2 summationdisplay y =1 x/y = (2 / 9) * x * 3 / 2 = 1 3 x, x = 1 , 2 . p Y ( y ) = 2 summationdisplay x =1 p ( x, y ) = (2 / 9) 2 summationdisplay x =1 x/y = (2 / 9) * (1 /y ) * 3 = 2 3 y , y = 1 , 2 . (c) P ( X > 1 | Y = 1) = P ( X > 1 , Y = 1) P ( Y = 1) = P ( X = 2 , Y = 1) P ( Y = 1) = p (2 , 1) p Y (1) = (2 / 9)(2 / 1) (2 / 3) = 2 3 . (d) The expected values are given by E [ X ] = 2 summationdisplay x =1 xp X ( x ) = 1 * 1 / 3 + 2 * 2 / 3 = 5 / 3 ....
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HW 22 Answers (8.1) - Math331, Spring 2008 Instructor:...

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