概率论与统计6-3

单击此处编辑母版标题样式,*,单击此处编辑母版文本样式,第二级,第三级,第四级,第五级,6.3,，和 分布,一、常见分布,二、概率分布的分位数,三、小结,一、常见分布,定义,6.3.1,性质,1,(此性质可以推广到多个随机变量的情形),性质,2,性质,3,同理,相互独立,则,t,分布,又称,学生氏,(,Student,),分布,.,2.,定义,6.3.2,当,n,充分大时,其图形类似于标准正态分布的变量的概率密度图形.,t,分布,具有下列性质：,性质,1,设 ,则当 时有,性质,2,设 ，是,T,的概率密度，,则,此性质说明，当 时，,T,分布的极限,分布是标准正态分布。,于是,3.,定义,6.3.3,(1),(2),(3),这说明,F,分布极限分布也是正态分布.,例,3,二、概率分布的分位数,根据正态分布的对称性知,附表,3,只详列到,n,=45,为止.,例如,利用上述公式,费歇资料,而查详表可得,费歇(,R.A.Fisher,),证明:,由,t,分布的对称性知,证明,三、小结,1.三个来自正态分布的抽样分布,:,2.上侧分位数的概念.,的,定义,性质,.,附表,2-1,标准正态分布表,z,0.00,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0,1.1,1.2,1.3,1.4,1.5,1.6,0.5000,0.5398,0.5793,0.6179,0.6554,0.6915,0.7257,0.7580,0.7881,0.8159,0.8413,0.8643,0.8849,0.9032,0.9192,0.9332,0.9452,0.5040,0.5438,0.5832,0.6217,0.6591,0.6950,0.7291,0.7611,0.7910,0.8186,0.8438,0.8665,0.8869,0.9049,0.9207,0.9345,0.9463,0.5080,0.5478,0.5871,0.6255,0.6628,0.6985,0.7324,0.7642,0.7939,0.8212,0.8461,0.8686,0.8888,0.9066,0.9222,0.9357,0.9474,0.5120,0.5517,0.5910,0.6293,0.6664,0.7019,0.7357,0.7673,0.7967,0.8238,0.8485,0.8708,0.8907,0.9082,0.9236,0.9370,0.9484,0.5160,0.5557,0.5948,0.6331,0.6700,0.7054,0.7389,0.7703,0.7995,0.8264,0.8508,0.8729,0.8925,0.9099,0.9251,0.9382,0.9495,0.5199,0.5596,0.5987,0.6368,0.6736,0.7088,0.7422,0.7734,0.8023,0.8289,0.8531,0.8749,0.8944,0.9115,0.9265,0.9394,0.9505,0.5239,0.5636,0.6026,0.6406,0.6772,0.7123,0.7454,0.7764,0.8051,0.8315,0.8554,0.8770,0.8962,0.9131,0.9278,0.9406,0.9515,0.5279,0.5675,0.6064,0.6443,0.6808,0.7157,0.7486,0.7794,0.8078,0.8340,0.8577,0.8790,0.8980,0.9147,0.9292,0.9418,0.9525,0.5319,0.5714,0.6103,0.6480,0.6844,0.7190,0.7517,0.7823,0.8106,0.8365,0.8599,0.8810,0.8997,0.9162,0.9306,0.9430,0.9535,0.5359,0.5753,0.6141,0.6517,0.6879,0.7224,0.7549,0.7852,0.8133,0.8389,0.8621,0.8830,0.9015,0.9177,0.9319,0.9441,0.9545,1.645,附表,2-2,标准正态分布表,z,0.00,0.01,0.02,0.03,0.04,0.05,0.06,0.07,0.08,0.09,1.6,1.7,1.8,1.9,2.0,2.1,2.2,2.3,2.4,2.5,2.6,2.7,2.8,2.9,3.0,0.9452,0.9554,0.9641,0.9713,0.9772,0.9821,0.9861,0.9893,0.9918,0.9938,0.9953,0.9965,0.9974,0.9981,0.9987,0.9463,0.9564,0.9648,0.9719,0.9778,0.9826,0.9864,0.9896,0.9920,0.9940,0.9955,0.9966,0.9975,0.9982,0.9990,0.9474,0.9573,0.9656,0.9726,0.9783,0.9830,0.9868,0.9898,0.9922,0.9941,0.9956,0.9967,0.9976,0.9982,0.9993,0.9484,0.9582,0.9664,0.9732,0.9788,0.9834,0.9871,0.9901,0.9925,0.9943,0.9957,0.9968,0.9977,0.9983,0.9995,0.9495,0.9591,0.9671,0.9738,0.9793,0.9838,0.9871,0.9904,0.9927,0.9945,0.9959,0.9969,0.9977,0.9984,0.9997,0.9505,0.9599,0.9678,0.9744,0.9798,0.9842,0.9878,0.9906,0.9929,0.9946,0.9960,0.9970,0.9978,0.9984,0.9698,0.9515,0.9608,0.9686,0.9750,0.9803,0.9846,0.9881,0.9909,0.9931,0.9948,0.9961,0.9971,0.9979,0.9985,0.9998,0.9525,0.9616,0.9693,0.9756,0.9808,0.9850,0.9884,0.9911,0.9932,0.9949,0.9962,0.9972,0.9979,0.9985,0.9999,0.9535,0.9625,0.9700,0.9762,0.9812,0.9854,0.9887,0.9913,0.9934,0.9951,0.9963,0.9973,0.9980,0.9986,0.9999,0.9545,0.9633,0.9706,0.9767,0.9817,0.9853,0.9890,0.9916,0.9936,0.9952,0.9964,0.9974,0.9981,0.9986,1.0000,1.96,附表,3-1,=0.25,0.10,0.05,0.025,0.01,0.005,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,1.323,2.773,4.108,5.385,6.626,7.841,9.037,10.219,11.389,12.549,13.701,14.845,15.984,17.117,18.245,19.369,2.706,4.605,6.251,7.779,9.236,10.645,12.017,13.362,14.684,15.987,17.275,18.549,19.812,20.064,22.307,23.542,3.841,5.991,7.815,9.488,11.071,12.592,14.067,15.507,16.919,18.307,19.675,21.026,22.362,23.685,24.996,26.296,5.024,7.378,9.348,11.143,12.833,14.449,16.013,17.535,19.023,20.483,21.920,23.337,24.736,26.119,27.488,28.845,6.635,9.210,11.345,13.277,15.086,16.812,18.475,20.090,21.666,23.209,24.725,26.217,27.688,29.141,30.578,32.000,7.879,10.597,12.838,14.860,16.750,18.548,20.278,21.955,23.589,25.188,26.757,28.299,29.891,31.319,32.801,34.267,分布表,17.535,=0.995,0.99,0.975,0.95,0.90,0.75,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,0.010,0.072,0.207,0.412,0.676,0.989,1.344,1.735,2.156,2.603,3.074,3.565,4.075,4.601,5.142,0.020,0.115,0.297,0.554,0.872,1.239,1.646,2.088,2.558,3.053,3.571,4.107,4.660,5.229,5.812,0.001,0.051,0.216,0.484,0.831,1.237,1.690,2.180,2.700,3.247,3.816,4.404,5.009,5.629,6.262,6.908,0.004,0.103,0.352,0.711,1.145,1.635,2.167,2.733,3.325,3.940,4.575,5.226,5.892,6.571,7.261,7.962,0.016,0.211,0.584,1.064,1.610,2.204,2.833,3.490,4.168,4.865,5.578,6.304,7.042,7.790,8.547,9.312,0.102,0.575,1.213,1.923,2.675,3.455,4.255,5.071,5.899,6.737,7.584,8.438,9.299,10.165,11.037,11.912,3.247,附表,3-2,分布表,=0.25,0.10,0.05,0.025,0.01,0.005,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,20.489,21.605,22.718,23.828,24.935,26.039,27.141,28.241,29.339,30.435,31.528,32.620,33.711,34.800,35.887,36.973,24.769,25.989,27.204,28.412,29.615,30.813,32.007,33.196,34.382,35.563,36.741,37.916,39.087,40.256,41.422,42.585,27.587,28.869,30.144,31.410,32.671,33.924,35.172,36.415,37.652,38.885,40.113,41.337,42.557,43.773,44.985,46.194,30.191,31.526,32.852,34.170,35.479,36.781,38.076,39.364,40.646,41.923,43.194,44.461,45.712,46.979,48.232,49.480,33.409,34.805,36.191,37.566,38.932,40.289,41.638,42.980,44.314,45.642,46.96