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# ma316f03hw9 - MA 316 MATHEMATICAL PROBABILITY ASSIGNMENT#9...

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Unformatted text preview: MA 316: MATHEMATICAL PROBABILITY ASSIGNMENT #9 SOLUTIONS: SECTIONS 4.2 and 4.3 FALL 2003 4.17: If f ( x ) = 1 / 3 for x = 1 , 2 , 3 then the density function for Y = 2 X + 1 is P ( Y = y ) = P (2 X + 1 = y ) = P ( X = ( y- 1) / 2) = 1 / 3 for y = 3 , 5 , 7 . 4.20: If f ( x 1 ,x 2 ) = x 1 x 2 / 36 for x 1 ,x 2 = 1 , 2 , 3 then the joint density function for Y 1 = X 1 X 2 and Y 2 = X 2 is g ( y 1 ,y 2 ) = y 1 / 36 for y 1 = y 2 , 2 y 2 , 3 y 2 and y 2 = 1 , 2 , 3. The marginal density for Y 1 is then g (1) = 1 / 36 ,g (2) = 4 / 36 ,g (3) = 6 / 36 ,g (4) = 4 / 36 ,g (6) = 12 / 36 , and g(9) = 9 / 36 . 4.21: If X 1 ∼ b ( n 1 ,p ) and X 2 ∼ b ( n 2 ,p ) are independent random variables then the joint density of X 1 and X 2 is P ( X 1 = x 1 ,X 2 = x 2 ) = n 1 x 1 ¶ p x 1 (1- p ) n 1- x 1 · n 2 x 2 ¶ p x 2 (1- p ) n 2- x 2 = n 1 x 1 ¶ n 2 x 2 ¶ p x 1 + x 2 (1- p ) n 1 + n 2- ( x 1 + x 2 ) ....
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ma316f03hw9 - MA 316 MATHEMATICAL PROBABILITY ASSIGNMENT#9...

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