Homework9 - HOMEWORK PROBLEMS#9 SOLUTIONS TO EVEN PROBLEMS...

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HOMEWORK PROBLEMS #9 SOLUTIONS TO EVEN PROBLEMS 38. Y U(0 , 1) (a) Then f ( y ) = ( 1 1 - 0 , 0 < y < 1 , 0 , elsewhere. and F ( y ) = Z y -∞ f ( t ) dt = 0 , y 0 y, 0 < y < 1 1 , y 1 . (b) Since 0 a + b 1 and 0 a 1, we have that P ( a Y a + b ) = F ( a + b ) - F ( a ) = ( a + b ) - a = b , which depends only on the value of b . 42. We want to find y such that F ( y ) = 0 . 5. Therefore, y - θ 1 θ 2 - θ 1 = 0 . 5, solving for y we get that the median is y = φ 0 . 5 = θ 2 + θ 1 2 . 44. (a) We must have that 1 = Z 2 - 2 kdy = ky | 2 - 2 = k (2 - ( - 2)) = 4 k . Therefore, k = 1 4 . (b) F ( y ) = Z y -∞ f ( t ) dt = 0 , y < - 2 R y - 2 1 4 dt = y +2 4 , - 2 y 2 1 , y > 2 . 52. Y U(50 , 70), so E ( Y ) = 50+70 2 = 60 and Var( Y ) = (70 - 50) 2 12 = 100 3 33 . 33. 68. (a) Y N(2 . 4 ,. 8 2 ). Therefore, P ( Y > 3 . 0) = P ± Y - 2 . 4 . 8 > 3 . 0 - 2 . 4 . 8 ) = P ( Z > . 75) 0 . 2266. 70. (a) By independentce,
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This note was uploaded on 02/23/2011 for the course MATH 444 taught by Professor Any during the Fall '10 term at Roosevelt.

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