chapter3 - 1 Chapter 3 31. (a) y 0 20 80 ow pY (y) 0.6 0.3...

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1 Chapter 3 3–1. (a) y p Y ( y ) 0 0.6 20 0.3 80 0.1 ow 0 (b) E ( Y ) = X y y · p Y ( y ) = 14 V ( Y ) = X y y 2 · p Y ( y ) - (14) 2 = 564 3–2. Let Profit = P = 10 + 2 X P ( P p ) = P (10 + 2 X p ) = P ± X p - 10 2 = Z p - 10 2 0 x 18 dx F P ( p ) = x 2 36 p - 10 2 0 = 1 144 ( p 2 - 20 p + 100) f P ( p ) = 1 72 ( p - 10);10 p 22 = 0; ow 3–3. (a) P ( T < 1) = 1 - e - 1 / 4 = 0 . 221 (b) E [ P ] = 200 - 200 P ( T < 1) = 155 . 80 3–4. (a) x p X ( x ) y = 2000(12 - x ) p Y ( y ) 10 0.1 4000 0.1 11 0.3 2000 0.3 12 0.4 0 0.4 13 0.1 - 2000 0.1 14 0.1 - 4000 0.1 ow 0 ow 0 (b) E ( X ) = 10(0 . 1) + 11(0 . 3) + 12(0 . 4) + 13(0 . 1) + 14(0 . 1) = 11 . 8 days V ( X ) = 10 2 (0 . 1) + 11 2 (0 . 3) + 12 2 (0 . 4) + 13 2 (0 . 1) + 14 2 (0 . 1) - (11 . 8) 2 = 1 . 16 days 2
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2 E ( Y ) = (4000)(0 . 1) + (2000)(0 . 3) + 0(0 . 4) + ( - 2000)(0 . 1) + ( - 4000)(0 . 1) = $400 V ( Y ) = (4000) 2 (0 . 1) + (2000) 2 (0 . 3) + 0 2 (0 . 4) + ( - 2000) 2 (0 . 1) + ( - 4000) 2 (0 . 1) - 400 2 = 4 , 640 , 000($ 2 ) 3–5. F Z ( z ) = P ( Z z ) = P ( X 2 z ) = P ( | X | ≤ z ) = P (0 X z ) = R z 0 2 xe - x 2 dx Let u = x 2 , du = 2 xdx , so F Z ( z ) = Z z 0 e - u du = 1 - e z f Z ( z ) = e - z ; z 0 = 0; ow 3–6. (a) E ( D i ) = 9 X d =0 d · p D i ( d ) = 1 10 (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9) = 4 . 5 (b) V ( D i ) = 9 X d =0 d 2 · p D i ( d ) - (4 . 5) 2 = 1 10 [1 2 + 2 2 + 3 2 + 4 2 + 5 2 + 6 2 + 7 2 + 8 2 + 9 2 ] - (20 . 25) = 8 . 25 (c) d y y p Y ( y ) 0 4 0 0.2 1 3 1 0.2 2 2 2 0.2 3 1 3 0.2 4 0 4 0.2 5 0 ow 0 6 1 7 2 8 3 9 4 E ( Y ) = 2 10 (1 + 2 + 3 + 4) = 2 V ( Y ) = 2 10 (1 2 + 2 2 + 3 2 + 4 2 ) - 4 = 2
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3 3–7. R = Revenue / Gal R = 0 . 92; A < 0 . 7 = 0 . 98; A 0 . 7 E ( R ) = 0 . 92 P ( A < 0 . 7) + 0 . 98 P ( A 0 . 7) = 0 . 92(0 . 7) + 0 . 98(0 . 3) = 93 . 8c | / gal. 3–8. M X ( t ) = Z β e tx 1 θ e - 1 θ ( x - β ) dx = 1 θ e β/θ Z β e - x ( 1 θ - t ) dx = 1 θ ± 1 θ - t - 1 e βt , for 1 θ - t > 0 M 0 X ( t ) = 1 θ ± 1 - θt θ - 2 e βt 1 - θt θ β + 1 M 00 X ( t ) = 1 θ ± 1 - θt θ - 3 e βt " ± 1 - θt θ 2 β 2 + ± 1 - θt θ β + 2 + ± 1 - θt θ β # E ( X ) = M 0 X (0) = β + θ V ( X ) = M 00 X (0) - ( β
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This homework help was uploaded on 04/09/2008 for the course ENGR, STAT 320, 262, taught by Professor Harris during the Spring '08 term at Purdue University-West Lafayette.

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chapter3 - 1 Chapter 3 31. (a) y 0 20 80 ow pY (y) 0.6 0.3...

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