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確率論及統計論 >> Article details

2016/05/12

確率・統計拡張問題2

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病気の判定をする検査の方法の評価関数を設計しなさい。
設計が検査の性格および制約条件を満たしていることを論述しなさい。

病気の人の割合(A)
病気でないのに陽性とでる確率(B)
病気なのに陰性とでる確率(C)

検査の性格としてB>Cを制約条件とする。

解答例 下表のE/G

 
病気の人の存在確率A病気でないのに陽性と出る確率B病気なのに陰性とでる確率C陽性と出たときの病気の確率(D)病気の存在確率に対する倍率(E=D/C)陰性と出たときの病気の確率(F)病気の存在確率に対する倍率(G=F/A)評価関数(E/G)
0.0010.10.010.0098126679.8126672611.1111E-050.0011110998831.498662
0.010.10.010.0909090919.0909090910.0001110990.011109877818.2727273
0.10.10.010.5238095245.2380952380.0011098780.11098779147.1952381
0.20.10.010.7122302163.5611510790.0022172950.2217294916.06079137
0.40.10.010.8684210532.1710526320.0044247790.4424778764.906578947
0.80.10.010.9753694581.2192118230.0088105730.8810572691.383805419
        
0.0010.050.010.01943462919.434628981.05262E-050.0010526218463.09187
0.010.050.010.16666666716.666666670.0001052520.0105252081583.5
0.10.050.010.68756.8750.0010515250.10515247165.38125
0.20.050.010.8319327734.1596638660.002100840.21008403419.8
0.40.050.010.9295774652.3239436620.0041928720.4192872125.542605634
0.80.050.010.9875311721.2344139650.0083507310.8350730691.478210723
        
0.0010.20.010.0049305244.9305244291.24998E-050.0012499843944.468848
0.010.20.010.0476190484.7619047620.0001249840.012498438381
0.10.20.010.354838713.5483870970.0012484390.12484394528.42258065
0.20.20.010.5530726262.7653631280.0024937660.24937655911.08910615
0.40.20.010.767441861.9186046510.0049751240.4975124383.856395349
0.80.20.010.9519230771.1899038460.009900990.990099011.201802885
        
0.0010.40.010.0024713552.4713547521.66664E-050.0016666391482.837565
0.010.40.010.0243902442.439024390.0001666390.016663889146.3658537
0.10.40.010.2156862752.1568627450.0016638940.16638935112.9627451
0.20.40.010.3822393821.9111969110.0033222590.3322259145.752702703
0.40.40.010.6226415091.5566037740.0066225170.6622516562.350471698
0.80.40.010.9082568811.1353211010.0131578951.3157894740.862844037
        
0.0010.10.0050.0098617379.861737455.55552E-060.0011111058875.613014
0.010.10.0050.0913262969.1326296475.55525E-050.011110494821.9823313
0.10.10.0050.5250659635.2506596310.0005552470.11104941747.28218997
0.20.10.0050.7132616493.5663082440.0011098780.22197558316.06621864
0.40.10.0050.8689956332.1724890830.0022172950.443458984.898962882
0.80.10.0050.9754901961.2193627450.0044247790.8849557521.377879902
        
0.0010.10.020.0097145129.7145122922.22217E-050.0011110868743.255353
0.010.10.020.0900735299.0073529410.0002221730.011108643810.8419118
0.10.10.020.5212765965.2127659570.0022172950.11086474547.01914894
0.20.10.020.7101449283.5507246380.0044247790.22123893816.04927536
0.40.10.020.8672566372.1681415930.0088105730.4405286344.921681416
0.80.10.020.9751243781.2189054730.0174672490.8733624451.395646766
        
0.0010.10.040.0095181449.5181439624.44425E-050.0011110628566.710291
0.010.10.040.088397798.8397790060.0004442470.011106175795.9337017
0.10.10.040.5161290325.1612903230.0044247790.11061946946.65806452
0.20.10.040.7058823533.5294117650.0088105730.22026431716.02352941
0.40.10.040.8648648652.1621621620.0174672490.4366812234.951351351
0.80.10.040.9746192891.2182741120.0343347640.8583690991.41928934
        
0.0010.10.080.0091251749.1251735778.8881E-050.0011110128213.386233
0.010.10.080.0850277268.5027726430.0008880990.011101243765.9297597
0.10.10.080.5054945055.0549450550.0088105730.11013215945.8989011
0.20.10.080.6969696973.4848484850.0174672490.21834061115.96060606
0.40.10.080.8598130842.149532710.0343347640.4291845495.008411215
0.80.10.080.9735449741.2169312170.0663900410.8298755191.466402116

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