hw6solu_427

# hw6solu_427 - HW 6 Solutions 4.63 a. If a customers calls...

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HW 6 Solutions 4.63 a. If a customer’s calls are typically short, the first calling plan makes more sense. If a customer’s calls are somewhat longer, then the second plan makes more sense, viz. 99¢ is less than 20min(10¢/min) = \$2 for the first 20 minutes under the first (flat–rate) plan. b, h 1 (X) = 10X, while h 2 (X) = 99 for X ≤ 20 and 99 + 10(X – 20) for X > 20. With μ = 1/λ for the exponential distribution, it’s obvious that E*h 1 (X)± = 10E*X± = 10μ. On the other hand, E[h 2 (X)] = 99 + 20 ) 20 ( 10 dx e x x = 99 + 20 10 e = 99 + 10μ e –20/μ . When μ = 10, E*h 1 (X)] = 100¢ = \$1.00 while E[h 2 (X)] = 99 + 100 e –2 ≈ \$1.13. When μ = 15, E*h 1 (X)] = 150¢ = \$1.50 while E[h 2 (X)] = 99 + 150 e –4/3 ≈ \$1.39. As predicted, the first plan is better when expected call length is lower, and the second plan is better when expected call length is somewhat higher. 4.67 = 24, 2 = 144  = 24,  2 = 144 = 6, = 4 a P(12 X 24) = F(4;4) – F(2;4) = .424 b. P(X 24) = F(4;4) = .567, so while the mean is 24, the median is less than 24, since P(X

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## This note was uploaded on 03/22/2011 for the course STAT 427 taught by Professor Staff during the Spring '08 term at Ohio State.

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hw6solu_427 - HW 6 Solutions 4.63 a. If a customers calls...

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