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ISE361_HW3answers_F03

ISE361_HW3answers_F03 - ISE 361 Homework Three 8 Fall 2003...

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ISE 361 Homework Three Fall 2003 8. Y = 3: SSS; Y = 4: FSSS; Y = 5: FFSSS, SFSSS; Y = 6: SSFSSS, SFFSSS, FSFSSS, FFFSSS; Y = 7: SSFFS, SFSFSSS<SFFFSSS, FSSFSSS, FSFFSSS, FFSFSSS, FFFFSSS 14. a) Summation p(n) = K[1+2+3+4+5] = 15K =1 K= 1/15 n= 1 to 5 b) P(Y<=3) = p(1) + p(2) + p(3) = 6/15 = 0.40 c) P(2<=Y<=4) = p(2) + p(3) + p(4) = 9/15 = 0.60 d) Summation (y 2 /50) = 1/50[1+4+9+16+25) = 55/50 Not equal to 1; NO y = 1to5 22. a) P(X = 2) = .39 - .19 = 0.20 b) P(X > 3) = 1 - .67 = 0.33 c) P(2 <= X <= 5) = .92 - .19 = 0.78 d) P(2 < X < 5) = .92 - .39 = 0.53 28. a) E(X) = Summation n p(n) = (0)(.08) + (1)(.15) + (2)(.45) + (3)(.27) + (4)(.05) = 2.06 n = 0 t o4 b) V(X) = Summation (n-2.06) 2 p(n) = (0 – 2.06) 2 (.08) +…+ (4 – 2.06) 2 (.05) = 0.9364 n = 0 to 4 c) SD = (.9364) 1/2 = 0.9677 d) V(X) = [Summation n 2 p(n)] – (2.06) 2 = 5.18 – 4.2436 = 0.9364 n= 0to4 34. Let h(X) denote the net revenue (sales revenue – order cost) as a function of X. Then h 3 (X) and h 4 (X) are the net revenue for 3 and 4 copies purchased, respectively. For x=1 or 2, h 3 (X) = 2x – 3, but at x = 3,4,5,6 the revenue plateaus. Following similar reasoning, h 4 (X) = 2x – 4 for x= 1,2,3, but plateaus at 4 for x= 4,5,6. x 1 2 3 4 5 6 h 3 (x) -1 1 3 3 3 3 h 4 (x) -2 0 2 4 4 4 p(x) 1/15 2/15 3/15 4/15 3/15 2/15 E(h 3 (x))= Summation h 3 (x) p(x) = (-1)(1/15)+…+ (3)(2/15) = 2.4667 x = 1 to 6 E(h 4
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