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# HW #9 - Homework-09 38 Z = X Y z = E(Z = E(X Y = E(X E(Y...

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Homework-09 38. Z = X + Y , μ z = E( Z ) = E( X + Y ) = E( X ) + E( Y ) = μ x + μ y = 12 + 5 = 17 , σ z = σ 2 z = Var( Z ) = Var( X + Y ) indep . = Var( X ) + Var( Y ) indep . = σ 2 x + σ 2 y = (1 . 4) 2 + (0 . 6) 2 = 2 . 32 = 1 . 523 . 39. Let { V 1 , V 2 , . . . , V 10 } indicates the volumes of ten drinks from the drink dispenser. They are given to be identically distributed (same dispenser) and independent of each other. (1) The total volume is given by the sum, T = V 1 + V 2 + · · · + V 10 . E( T ) = 10(8) = 80. σ T = 10(0 . 15) 2 (2) The average volume is given by ¯ V = 1 / 10( V 1 + V 2 + · · · + V 10 ). E( ¯ V ) = 8. σ ¯ V = (0 . 15) 2 10 . 40. Let R be the revenue of a flight chosen at random, i.e. R = 1800 X 1 + 1160 X 2 + 525 X 3 . μ R = E( R ) = 1800 μ 1 + 1160 μ 2 + 525 μ 3 = 1800(6) + 1160(61 . 3) + 525(401 . 7) = 292800 . 5 . σ 2 R = Var( R ) = (1800) 2 σ 2 1 + (1160) 2 σ 2 2 + (525) 2 σ 2 3 = (1800) 2 (1 . 5) 2 + (1160) 2 (4 . 8) 2 + (525) 2 (26 . 5) 2 = 231850280 . 25 σ R = 231850280 . 25 = 15226 . 63063 . 42. Refer to problem #41. a. (Recall that p x 2 | x 1 ( x 2 | 1) = p (1 ,x 2 ) p 1 (1) , x 2 = 0 , 1 , 2 , 3.) x 2 p x 2 | x 1 ( x 2 | 1) 0 0.04/0.60=1/15 1 0.36/0.60=3/5 2 0.18/0.60=3/10 3 0.02/0.60=1/30 b. Similarly, p x 1 | x 2 ( x 1 | 2) = p ( x 1 , 2) p 2 (2) , x 1 = 0 , 1 , 2 , 3 x 1 p x 1 | x 2 ( x 1 | 2) 0 0.03/0.27=1/9 1 0.18/0.27=2/3 2 0.04/0.27=4/27 3 0.02/0.27=2/27

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c. Based on a. and b.
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