ENME 392 - Homework 4 - Sp12_Solutions

ENME 392 - Homework 4 - Sp12_Solutions - ENME392 Spring...

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ENME392 Spring 2012 Homework 4 Solutions Total number of points: 100 1. Chapter 3 : 3.39 (leave as a formula) (4 pts) sack of fruit with 3 oranges X, 2 apples Y, 3 bananas B 8 total fruit, take 4 pieces X = # oranges, Y = # of apples (a) f(x,y) = ? same as example 3.14 p. 92 3 2 3 x y 4-x-y f(x,y) = 8 4             for x = 0, 1, 2, 3; y = 0, 1, 2 (b) P(x+y < 2) = f(1, 0) + f(0,1) + f(1, 1) + f(2, 0) + f(0,2) There is no f(0,0) since there are only 3 bananas. 3 2 3 3 2 3 3 2 3 3 2 3 3 2 3 1 0 3 0 1 3 1 1 2 2 0 2 0 2 2 f(x,y) = 8 4                     + + + +                                               = (3*1*1 + 1*2*1 + 3*2*3 + 3*1*3 + 1*1*3) / (8*7*6*5 / 4*3*2) = (3 + 2 + 18 + 9 + 3) / 70 = 35 / 70 = ½ 2. Chapter 3 : 3.40 (6 pts) X proportion of time drive-in in use y proportion of time walk-in in use 2 2 0 1 0 1 3 0 ( x y ), x , y f ( x, y ) ,elsewhere + ≤ ≤ =
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(a) g(x) = 1 1 2 0 0 2 2 2 2 2 2 1 3 3 3 f ( x, y )dy ( x y )dy ( xy y / ) ( x ) -∞ = + = + = + (b) (c) P(X < ½) = 1 2 1 2 2 0 0 2 2 2 1 2 1 8 4 8 10 24 3 3 3 / / ( x )dx ( x / x ) ( / / ) / + = + = + = 3. Chapter 3 : 3.49 (6 pts) (a, b) Find g(x), h(y) f(x,y) x row totals 1 2 3 y 1 0.05 0.05 0.10 0.20 2 0.05 0.10 0.35 0.50 3 0.00 0.20 0.10 0.30 column totals 0.10 0.35 0.55 1.00 (c) P(Y = 3 | X = 2) = 0.2/0.35 Pay special attention to this example – this will be of frequent use later in the course. 4.
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ENME 392 - Homework 4 - Sp12_Solutions - ENME392 Spring...

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