Fundamentals of Probability and Statistics for Engineers

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