ch05 SOLUTION.doc - Chapter 5 Discrete Distributions 5.1 x...

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Chapter 5: Discrete Distributions 1 SOLUTIONS TO PROBLEMS IN CHAPTER 5 5.1 x P(x) x·P(x) (x-µ) 2 (x-µ) 2 ·P(x) 1 .238 .238 2.775556 0.6605823 2 .290 .580 0.443556 0.1286312 3 .177 .531 0.111556 0.0197454 4 .158 .632 1.779556 0.2811700 5 .137 .685 5.447556 0.7463152 µ = [x·P(x)] = 2.666 2 = (x-µ) 2 ·P(x) = 1.836444 = 836444 . 1 = 1.355155 5.2 x P(x) x·P(x) (x-µ) 2 (x-µ) 2 ·P(x) 0 .103 .000 7.573504 0.780071 1 .118 .118 3.069504 0.362201 2 .246 .492 0.565504 0.139114 3 .229 .687 0.061504 0.014084 4 .138 .552 1.557504 0.214936 5 .094 .470 5.053504 0.475029 6 .071 .426 10.549500 0.749015 7 .001 .007 18.045500 0.018046 µ = [x·P(x)] = 2.752 2 = (x-µ) 2 ·P(x) = 2.752496 = 752496 . 2 = 1.6591 5.3 x P(x) x·P(x) (x-µ) 2 (x-µ) 2 ·P(x) 0 .461 .000 0.913936 0.421324 1 .285 .285 0.001936 0.000552 2 .129 .258 1.089936 0.140602 3 .087 .261 4.177936 0.363480 4 .038 .152 9.265936 0.352106 E(x)=µ= [x·P(x)]= 0.956 2 = (x-µ) 2 ·P(x) = 1.278064 = 278064 . 1 = 1.1305 5.4 x P(x) x·P(x) (x-µ) 2 (x-µ) 2 ·P(x) 0 .262 .000 1.4424 0.37791 1 .393 .393 0.0404 0.01588 2 .246 .492 0.6384 0.15705 3 .082 .246 3.2364 0.26538 4 .015 .060 7.8344 0.11752 5 .002 .010 14.4324 0.02886 6 .000 .000 23.0304 0.00000 µ = [x·P(x)] = 1.201 2 = (x-µ) 2 ·P(x) = 0.96260 = 96260 . = .98112
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Chapter 5: Discrete Distributions 2 5.5 a) n = 4 p = .10 q = .90 P(x=3) = 4 C 3 (.10) 3 (.90) 1 = 4(.001)(.90) = .0036 b) n = 7 p = .80 q = .20 P(x=4) = 7 C 4 (.80) 4 (.20) 3 = 35(.4096)(.008) = .1147 c) n = 10 p = .60 q = .40 P(x > 7) = P(x=7) + P(x=8) + P(x=9) + P(x=10) = 10 C 7 (.60) 7 (.40) 3 + 10 C 8 (.60) 8 (.40) 2 + 10 C 9 (.60) 9 (.40) 1 + 10 C 10 (.60) 10 (.40) 0 = 120(.0280)(.064) + 45(.0168)(.16) + 10(.0101)(.40) + 1(.0060)(1) = .2150 + .1209 + .0403 + .0060 = .3822 d) n = 12 p = .45 q = .55 P(5 < x < 7) = P(x=5) + P(x=6) + P(x=7) = 12 C 5 (.45) 5 (.55) 7 + 12 C 6 (.45) 6 (.55) 6 + 12 C 7 (.45) 7 (.55) 5 = 792(.0185)(.0152) + 924(.0083)(.0277) + 792(.0037)(.0503) = .2225 + .2124 + .1489 = .5838 5.6 By Table A.2: a) n = 20 p = .50 P(x=12) = .120 b) n = 20 p = .30 P(x > 8) = P(x=9) + P(x=10) + P(x=11) + ...+ P(x=20) = .065 + .031 + .012 + .004 + .001 + .000 = .113 c) n = 20 p = .70 P(x < 12) = P(x=11) + P(x=10) + P(x=9) + ... + (Px=0) = .065 + .031 + .012 + .004 + .001 + .000 = .113 d) n = 20 p = .90 P(x < 16) = P(x=16) + P(x=15) + P(x=14) + ...+ P(x=0) = .090 + .032 + .009 + .002 + .000 = .133 e) n = 15 p = .40 P(4 < x < 9) = P(x=4) + P(x=5) + P(x=6) + P(x=7) + P(x=8) + P(x=9) = .127 + .186 + .207 + .177 + .118 + .061 = .876 f) n = 10 p = .60 P(x > 7) = P(x=7) + P(x=8) + P(x=9) + P(x=10) = .215 + .122 + .040 + .006 = .382 5.7 a) n = 20 p = .70 q = .30 µ = n p = 20(.70) = 14 = 2 . 4 ) 30 )(. 70 (. 20 q p n = 2.05 b) n = 70 p = .35 q = .65 µ = n p = 70(.35) = 24.5 = 925 . 15 ) 65 )(. 35 (. 70 q p n = 3.99
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Chapter 5: Discrete Distributions 3 c) n = 100 p = .50 q = .50 µ = n p = 100(.50) = 50 = 25 ) 50 )(. 50 (. 100 q p n = 5 5.8 a) n = 6 p = .70 x Prob 0 .001 1 .010 2 .060 3 .185 4 .324 5 .303 6 .118 b) n = 20 p = .50 x Prob 0 .000 1 .000 2 .000 3 .001 4 .005 5 .015 6 .037 7 .074 8 .120 9 .160 10 .176 11 .160 12 .120 13 .074 14 .037 15 .015 16 .005 17 .001
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Chapter 5: Discrete Distributions 4 18 .000 19 .000 20 .000 c) n = 8 p = .80 x Prob 0 .000 1 .000 2 .001 3 .009 4 .046 5 .147 6 .294 7 .336 8 .168 5.9 a) n = 20 p = .78 x = 14 20 C 14 (.78) 14 (.22) 6 = 38,760(.030855)(.00011338) = . 1356 b) n = 20 p = .75 x = 20
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Chapter 5: Discrete Distributions 5 20 C 20 (.75) 20 (.25) 0 = (1)(.0031712)(1) = .0032 c) n = 20 p = .70 x < 12 Use table A.2: P(x=0) + P(x=1) + . . . + P(x=11)= .000 + .000 + .000 + .000 + .000 + .000 + .000 + .001 + .004 + .012 + .031 + .065 = . 113 5.10 n = 16 p = .40 P(x > 9): from Table A.2: x Prob 9 .084 10 .039 11 .014 12 .004 13 .001 .142 P(3 < x < 6): x Prob 3 .047 4 .101 5 .162 6 .198 .508 n = 13 p = .88 P(x = 10) = 13 C 10 (.88) 10 (.12) 3 = 286(.278500976)(.001728) = .1376 P(x = 13) = 13 C 13 (.88) 13 (.12) 0 = (1)(.1897906171)(1) = .1898 Expected Value = µ = n p = 13(.88) = 11.44 5.11 n = 25 P = .60 a) x > 15 P(x > 15) = P(x = 15) + P(x = 16) + · · · + P(x = 25) Using Table A.2 n = 25, p = .80
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Chapter 5: Discrete Distributions 6 x Prob 15 .161 16 .151 17 .120 18 .080 19 .044 20 .020 21 .007 22 .002 .585 b) x > 20 from a): P(x > 20) = P(x = 21) + P(x = 22) + P(x = 23) + P(x = 24) + P(x = 25) = .007 + .002 + .000 + .000 + .000 = .009 c) P(x < 10) from Table A.2, x Prob.
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  • Summer '18
  • Keyur Popat
  • Poisson Distribution, Discrete probability distribution, C5-convertase, = P, + p, 4C3

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