Fundamentals of Probability and Statistics for Engineers

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Appendix C: Answers to Selected Problems 385CHAPTER 77.1 0.8477.3 (a) 0.9, (b) 0.7757.6 (a) 4.566 10 3 , (b) 0.8944, (c) 0.383, (d) 0.3857.9 X 2 is preferred in both cases7.14 0.00627.20 (a) 0.221(b)81f Y …y† ˆ …0:294†…2† 1=2 …y a† exp 1y a>:0; elsewherem Y ˆ a ‡ b7.22 0.1537.30 (a) 0.056, (b) 0.9897.34 0.125, 0, 0, 0.875. No partial failure is possible7.36 8 Z 1
386 Fundamentals of Probability and Statistics for Engineers9.79.119.149.159.209.229.249.269.309.329.349.369.38^ 1 is betterIt is biased, but unbiased as n !1a) 2 /n, b) 2 /n, c) 1 )/n, d) /n 2 /n,2 4 /na) 1b) 11X ,X 9kˆ1 1X 1 1 k 1X^A ML ˆ X 1) , ^AME ˆ X 1^ ˆ 0:13sec 1a) ^ ML ˆ ^ ME ˆ T t 0 ) 1b) ^T 0ML ˆ T 1) , ^T 0ME ˆ T 1/)c)^ ML ˆ‰T T …1† Š1 ; ^T 0ML ˆ T …1†^ ME ˆ…M 2 T 2 † 1=2 ; ^T 0ME ˆ T …M 2 T 2 † 1=22) 1/2a) l 1, 2 ˆ 63:65, 81:55, b) l 1, 2 ˆ 70:57, 84:43, c) l 1, 2 ˆ 77:74, 89:46a) 9.16, b) l 1, 2 ˆ 8:46, 9:86a) l 1, 2 ˆ 1072, 1128, b) l 1, 2 ˆ 1340, 6218 and l 1 ˆ 1478384CHAPTER 1010.1 More likely to be accepted at ˆ 0:0110.3 Hypothesis is accepted10.5 Hypothesis is accepted10.8 Poisson hypothesis is rejected10.10 Gamma hypothesis is accepted10.12 Normal hypothesis is accepted10.14 Poisson hypothesis is accepted10.16 Hypothesis is acceptedCHAPTER 1111.1 (a)^B ˆXniˆ1x i Y i!X nx 2 iiˆ1! 1TLFeBOOK
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ContentsPREFACExiii1 INTRODUCTION 1
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Contentsix6.1.2 Geometric Distribut
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ContentsxiAPPENDIX A: TABLES 365A.1
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PrefaceThis book was written for an
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1IntroductionAt present, almost all
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Introduction 3may be rejected at th
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Part AProbability and Random Variab
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8 Fundamentals of Probability and S
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14 Fundamentals of Probability and
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Basic Probability Concepts 19where
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