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§3.2统计量与抽样分布统计量的定义§3.2统计量与抽样分布统计量的定义是不是例1是不是例12.

几个常用统计量(样本矩)的定义(1)样本均值(2)样本方差它反映了总体均值的信息它反映了总体方差的信息2.几个常用统计量(样本矩)的定义(1)样本均值(2)样本(3)样本标准差(4)

样本k阶(原点)矩(5)样本k阶中心矩(3)样本标准差(4)样本k阶(原点)矩(5)样本k2.2抽样分布统计量是n维随机变量的函数，作为一个随机变量，它也有自己的概率分布。通常把统计量的分布称为抽样分布。设总体X的分布函数已知，如果对任意容量为n的样本，能求出给定的统计量的分布函数，则称该分布函数为的精确分布。

2.2抽样分布统计量是n维随1．样本均值的分布

正态总体的几个统计量的精确分布2．分布

3．t分布

4．F分布

1．样本均值的分布正态总体的几个统计量的精确分布2．分1.样本均值的分布设，是来自总体X的样本，由于正态变量的线性函数仍为正态变量，故

，通常称为总体的标准误差，记作

1.样本均值的分布设，标准正态分布的上侧临界值

标准正态分布的双侧临界值

yxo图3-3yxo图3-4标准正态分布的上侧临界值yxo图3-3yxo图3-42．分布

2．分布分布的上侧临界值

图3-6oyx分布的上侧临界值图3-6oyx定理１

设是来自正态总体的样本，则1o

样本均值与样本方差相互独立；2o

定理１性质1(此性质可以推广到多个随机变量的情形)性质1(此性质可以推广到多个随机变量的情形)t分布又称学生氏(Student)分布.学生氏资料2.t分布又称学生氏(Student)分布.学生氏资料2.当n充分大时,其图形类似于标准正态变量概率密度的图形.当n充分大时,其图形类似于标准正态变量概率密度的图形.定理2

设是来自正态总体的样本，则统计量

定理2定理3

设和是来自正态总体和的样本，，且两者相互独立，则统计量

和

分别为两个总体的样本方差

定理3和分别为两个总体的样本方差称为样本均值差的标准误，记作，即。

分布的上侧临界值分布的双侧临界值称为样本均值差的标准误，分布的上侧临界值yxo图3-8yxo图3-9yxo图3-8yxo图3-9服从第一自由度为，第二自由度为的分布，记作3.F分布定义服从第一自由度为，第二自由度为的分布，记统计量与抽样分布-太行之路网站-欢迎您！课件F分布的上侧临界值是指满足下式的

定理４设，是正态总体的样本容量和样本方差；，是正态总体的样本容量和样本方差，且两个样本相互独立，则统计量F分布的上侧临界值是指满足下式的定理４设，附表2-1标准正态分布表z0.000.010.020.030.040.050.060.070.080.090.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.60.50000.53980.57930.61790.65540.69150.72570.75800.78810.81590.84130.86430.88490.90320.91920.93320.94520.50400.54380.58320.62170.65910.69500.72910.76110.79100.81860.84380.86650.88690.90490.92070.93450.94630.50800.54780.58710.62550.66280.69850.73240.76420.79390.82120.84610.86860.88880.90660.92220.93570.94740.51200.55170.59100.62930.66640.70190.73570.76730.79670.82380.84850.87080.89070.90820.92360.93700.94840.51600.55570.59480.63310.67000.70540.73890.77030.79950.82640.85080.87290.89250.90990.92510.93820.94950.51990.55960.59870.63680.67360.70880.74220.77340.80230.82890.85310.87490.89440.91150.92650.93940.95050.52390.56360.60260.64060.67720.71230.74540.77640.80510.83150.85540.87700.89620.91310.92780.94060.95150.52790.56750.60640.64430.68080.71570.74860.77940.80780.83400.85770.87900.89800.91470.92920.94180.95250.53190.57140.61030.64800.68440.71900.75170.78230.81060.83650.85990.88100.89970.91620.93060.94300.95350.53590.57530.61410.65170.68790.72240.75490.78520.81330.83890.86210.88300.90150.91770.93190.94410.95451.645附表2-1标准正态分布表z0.000.010.020.030附表2-2标准正态分布表z0.000.010.020.030.040.050.060.070.080.091.61.71.81.92.02.12.22.32.42.52.62.72.82.93.00.94520.95540.96410.97130.97720.98210.98610.98930.99180.99380.99530.99650.99740.99810.99870.94630.95640.96480.97190.97780.98260.98640.98960.99200.99400.99550.99660.99750.99820.99900.94740.95730.96560.97260.97830.98300.98680.98980.99220.99410.99560.99670.99760.99820.99930.94840.95820.96640.97320.97880.98340.98710.99010.99250.99430.99570.99680.99770.99830.99950.94950.95910.96710.97380.97930.98380.98710.99040.99270.99450.99590.99690.99770.99840.99970.95050.95990.96780.97440.97980.98420.98780.99060.99290.99460.99600.99700.99780.99840.96980.95150.96080.96860.97500.98030.98460.98810.99090.99310.99480.99610.99710.99790.99850.99980.95250.96160.96930.97560.98080.98500.98840.99110.99320.99490.99620.99720.99790.99850.99990.95350.96250.97000.97620.98120.98540.98870.99130.99340.99510.99630.99730.99800.99860.99990.95450.96330.97060.97670.98170.98530.98900.99160.99360.99520.99640.99740.99810.99861.00001.96附表2-2标准正态分布表z0.000.010.020.030附表4-1=0.250.100.050.0250.010.005123456789101112131415161.3232.7734.1085.3856.6267.8419.03710.21911.38912.54913.70114.84515.98417.11718.24519.3692.7064.6056.2517.7799.23610.64512.01713.36214.68415.98717.27518.54919.81220.06422.30723.5423.8415.9917.8159.48811.07112.59214.06715.50716.91918.30719.67521.02622.36223.68524.99626.2965.0247.3789.34811.14312.83314.44916.01317.53519.02320.48321.92023.33724.73626.11927.48828.8456.6359.21011.34513.27715.08616.81218.47520.09021.66623.20924.72526.21727.68829.14130.57832.0007.87910.59712.83814.86016.75018.54820.27821.95523.58925.18826.75728.29929.89131.31932.80134.267分布表17.535附表4-1=0.250.100.050.0250.010.=0.9950.990.9750.950.900.75123456789101112131415160.0100.0720.2070.4120.6760.9891.3441.7352.1562.6033.0743.5654.0754.6015.1420.0200.1150.2970.5540.8721.2391.6462.0882.5583.0533.5714.1074.6605.2295.8120.0010.0510.2160.4840.8311.2371.6902.1802.7003.2473.8164.4045.0095.6296.2626.9080.0040.1030.3520.7111.1451.6352.1672.7333.3253.9404.5755.2265.8926.5717.2617.9620.0160.2110.5841.0641.6102.2042.8333.4904.1684.8655.5786.3047.0427.7908.5479.3120.1020.5751.2131.9232.6753.4554.2555.0715.8996.7377.5848.4389.29910.16511.03711.9123.247附表4-2分布表=0.9950.990.9750.950.900.7510.=0.250.100.050.0250.010.0051718192021222324252627282930313220.48921.60522.71823.82824.93526.03927.14128.24129.33930.43531.52832.62033.71134.80035.88736.97324.76925.98927.20428.41229.61530.81332.00733.19634.38235.56336.74137.91639.08740.25641.42242.58527.58728.86930.14431.41032.67133.92435.17236.41537.65238.88540.11341.33742.55743.77344.98546.19430.19131.52632.85234.17035.47936.78138.07639.36440.64641.92343.19444.46145.71246.97948.23249.48033.40934.80536.19137.56638.93240.28941.63842.98044.31445.64246.96348.27849.58850.89252.19153.48635.71837.15638.58239.99741.40142.79644.18145.55946.92848.29049.64550.99352.33653.67255.00356.32834.382附表4-3分布表=0.250.100.050.0250.010.005172附表3-1=0.250.100.050.0250.010.005123456789101112131415161.00000.81650.76490.74070.72670.71760.71110.70640.70270.69980.69740.69550.69380.69240.69120.69013.07771.88561.63771.53321.47591.43981.41491.39681.38301.37221.36341.35621.35021.34501.34061.33686.31382.92002.35342.13182.01501.94321.89461.85951.83311.81251.79591.78231.77091.76131.75311.745912.70624.30273.18242.77642.57062.44692.36462.30602.26222.22812.20102.17882.16042.14482.13152.119931.82076.96464.54073.74693.36493.14272.99802.89652.82142.76382.71812.68102.65032.62452.60252.583563.65749.92485.84094.60414.03223.70743.49953.35543.24983.16933.10583.05453.01232.97682.94672.9208分布表1.8125附表3-1=0.250.100.050.0250.010.附表3-2=0.250.100.050.0250.010.005123456789101112131415161.00000.81650.76490.74070.72670.71760.71110.70640.70270.69980.69740.69550.69380.69240.69120.69013.07771.88561.63771.53321.47591.43981.41491.39681.38301.37221.36341.35621.35021.34501.34061.33686.31382.92002.35342.13182.01501.94321.89461.85951.83311.81251.79591.78231.77091.76131.75311.745912.70624.30273.18242.77642.57062.44692.36462.30602.26222.22812.20102.17882.16042.14482.13152.119931.82076.96464.54073.74693.36493.14272.99802.89652.82142.76382.71812.68102.65032.62452.60252.583563.65749.92485.84094.60414.03223.70743.49953.35543.24983.16933.10583.05453.01232.97682.94672.92082.1315分布表附表3-2=0.250.100.050.0250.010.附表5-1分布表

1234567891012152024304012012345678910111213141516171819647.838.5117.4412.2210.018.818.077.577.216.946.726.556.416.306.206.126.045.955.92799.539.0016.0410.658.437.266.546.065.715.465.265.104.974.864.774.694.624.564.51864.239.1715.449.987.766.605.895.425.084.834.634.474.354.244.154.084.013.953.90899.639.2515.109.607.396.235.525.504.724.474.284.124.003.893.803.733.663.613.56921.839.3014.889.367.155.995.294.824.484.244.043.893.773.663.583.503.443.383.33937.139.3314.739.206.985.825.124.654.234.073.883.733.603.503.413.343.283.223.17948.239.3614.629.076.855.704.994.534.203.953.763.613.483.383.293.223.163.103.05956.739.3714.548.986.765.604.904.434.103.853.663.513.393.293.203.123.063.012.96963.339.3914.478.906.685.524.824.364.033.783.593.443.313.213.123.052.982.932.88968.639.4014.428.846.625.464.764.303.963.723.533.373.253.153.062.992.922.872.82976.739.4114.348.756.525.374.674.203.873.623.433.283.153.052.962.892.822.772.72984.939.4314.258.666.435.274.574.103.773.523.333.183.052.952.862.792.722.672.62993.139.4514.178.566.335.174.474.003.673.423.233.072.952.842.762.682.622.562.51997.239.4614.128.516.285.124.423.593.613.373.173.022.892.792.702.632.562.502.45100139.4614.088.466.235.074.363.893.563.313.122.962.842.732.642.572.502.442.39100639.4714.048.416.185.014.313.843.513.263.062.912.782.672.592.512.442.382.33101439.4913.958.316.074.904.203.733.393.142.942.792.662.552.462.382.322.262.20101839.5013.908.266.024.854.143.673.333.082.882.722.602.492.402.322.252.192.134.90附表5-1分布表12345678910

1234567891015202430406012012345678910111213141516171819161.418.5110.137.716.615.995.595.323.124.964.844.754.674.604.544.494.454.414.38199.519.009.556.945.795.144.744.464.264.103.983.893.813.743.683.633.595.553.52215.719.169.286.595.414.764.354.073.813.713.593.493.413.343.293.243.203.163.13224.619.259.126.395.194.534.123.843.633.483.363.263.183.113.063.012.962.932.90230.219.309.016.265.054.393.973.693.48

3.333.203.113.032.962.902.852.812.772.74234.019.338.946.164.954.283.873.583.373.223.093.002.922.852.792.742.702.662.63236.819.358.896.094.884.213.793.503.293.143.012.912.832.762.712.662.612.582.54238.919.378.856.044.824.153.733.443.233.072.952.852.772.702.642.592.552.512.4824.0519.388.816.004.774.103.683.393.183.022.902.802.712.652.592.542.492.462.42241.919.408.795.964.744.063.643.353.142.982.852.752.672.602.542.492.452.412.38245.919.438.705.864.623.942.513.223.012.852.722.622.532.462.402.352.312.272.23248.019.458.665.804.563.873.443.152.942.772.652.542.462.392.332.282.232.192.16249.119.458.645.774.533.843.413.122.902.742.612.512.422.352.292.242.192.152.11250.119.468.625.754.503.813.383.082.86

2.702.575.472.382.312.252.192.152.112.07151.119.478.595.724.463.773.343.042.832.662.532.432.342.272.202.152.102.062.03252.219.488.575.694.433.743.303.012.792.622.492.382.302.22

2.162.112.062.021.98253.319.498.555.664.403.703.272.972.752.582.452.342.252.182.112.062.011.971.93254.319.508.535.634.363.673.232.932.712.542.402.302.212.132.072.011.961.921.882.31附表5-2分布表1234567891015202430学生氏资料Born:13June1876inCanterbury,England

Died:16Oct1937inBeaconsfield,EnglandWilliamSealeyGosset学生氏资料Born:13June1876inCan§3.2统计量与抽样分布统计量的定义§3.2统计量与抽样分布统计量的定义是不是例1是不是例12.

几个常用统计量(样本矩)的定义(1)样本均值(2)样本方差它反映了总体均值的信息它反映了总体方差的信息2.几个常用统计量(样本矩)的定义(1)样本均值(2)样本(3)样本标准差(4)

样本k阶(原点)矩(5)样本k阶中心矩(3)样本标准差(4)样本k阶(原点)矩(5)样本k2.2抽样分布统计量是n维随机变量的函数，作为一个随机变量，它也有自己的概率分布。通常把统计量的分布称为抽样分布。设总体X的分布函数已知，如果对任意容量为n的样本，能求出给定的统计量的分布函数，则称该分布函数为的精确分布。

2.2抽样分布统计量是n维随1．样本均值的分布

正态总体的几个统计量的精确分布2．分布

3．t分布

4．F分布

1．样本均值的分布正态总体的几个统计量的精确分布2．分1.样本均值的分布设，是来自总体X的样本，由于正态变量的线性函数仍为正态变量，故

，通常称为总体的标准误差，记作

1.样本均值的分布设，标准正态分布的上侧临界值

标准正态分布的双侧临界值

yxo图3-3yxo图3-4标准正态分布的上侧临界值yxo图3-3yxo图3-42．分布

2．分布分布的上侧临界值

图3-6oyx分布的上侧临界值图3-6oyx定理１

设是来自正态总体的样本，则1o

样本均值与样本方差相互独立；2o

定理１性质1(此性质可以推广到多个随机变量的情形)性质1(此性质可以推广到多个随机变量的情形)t分布又称学生氏(Student)分布.学生氏资料2.t分布又称学生氏(Student)分布.学生氏资料2.当n充分大时,其图形类似于标准正态变量概率密度的图形.当n充分大时,其图形类似于标准正态变量概率密度的图形.定理2

设是来自正态总体的样本，则统计量

定理2定理3

设和是来自正态总体和的样本，，且两者相互独立，则统计量

和

分别为两个总体的样本方差

定理3和分别为两个总体的样本方差称为样本均值差的标准误，记作，即。

分布的上侧临界值分布的双侧临界值称为样本均值差的标准误，分布的上侧临界值yxo图3-8yxo图3-9yxo图3-8yxo图3-9服从第一自由度为，第二自由度为的分布，记作3.F分布定义服从第一自由度为，第二自由度为的分布，记统计量与抽样分布-太行之路网站-欢迎您！课件F分布的上侧临界值是指满足下式的

定理４设，是正态总体的样本容量和样本方差；，是正态总体的样本容量和样本方差，且两个样本相互独立，则统计量F分布的上侧临界值是指满足下式的定理４设，附表2-1标准正态分布表z0.000.010.020.030.040.050.060.070.080.090.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.60.50000.53980.57930.61790.65540.69150.72570.75800.78810.81590.84130.86430.88490.90320.91920.93320.94520.50400.54380.58320.62170.65910.69500.72910.76110.79100.81860.84380.86650.88690.90490.92070.93450.94630.50800.54780.58710.62550.66280.69850.73240.76420.79390.82120.84610.86860.88880.90660.92220.93570.94740.51200.55170.59100.62930.66640.70190.73570.76730.79670.82380.84850.87080.89070.90820.92360.93700.94840.51600.55570.59480.63310.67000.70540.73890.77030.79950.82640.85080.87290.89250.90990.92510.93820.94950.51990.55960.59870.63680.67360.70880.74220.77340.80230.82890.85310.87490.89440.91150.92650.93940.95050.52390.56360.60260.64060.67720.71230.74540.77640.80510.83150.85540.87700.89620.91310.92780.94060.95150.52790.56750.60640.64430.68080.71570.74860.77940.80780.83400.85770.87900.89800.91470.92920.94180.95250.53190.57140.61030.64800.68440.71900.75170.78230.81060.83650.85990.88100.89970.91620.93060.94300.95350.53590.57530.61410.65170.68790.72240.75490.78520.81330.83890.86210.88300.90150.91770.93190.94410.95451.645附表2-1标准正态分布表z0.000.010.020.030附表2-2标准正态分布表z0.000.010.020.030.040.050.060.070.080.091.61.71.81.92.02.12.22.32.42.52.62.72.82.93.00.94520.95540.96410.97130.97720.98210.98610.98930.99180.99380.99530.99650.99740.99810.99870.94630.95640.96480.97190.97780.98260.98640.98960.99200.99400.99550.99660.99750.99820.99900.94740.95730.96560.97260.97830.98300.98680.98980.99220.99410.99560.99670.99760.99820.99930.94840.95820.96640.97320.97880.98340.98710.99010.99250.99430.99570.99680.99770.99830.99950.94950.95910.96710.97380.97930.98380.98710.99040.99270.99450.99590.99690.99770.99840.99970.95050.95990.96780.97440.97980.98420.98780.99060.99290.99460.99600.99700.99780.99840.96980.95150.96080.96860.97500.98030.98460.98810.99090.99310.99480.99610.99710.99790.99850.99980.95250.96160.96930.97560.98080.98500.98840.99110.99320.99490.99620.99720.99790.99850.99990.95350.96250.97000.97620.98120.98540.98870.99130.99340.99510.99630.99730.99800.99860.99990.95450.96330.97060.97670.98170.98530.98900.99160.99360.99520.99640.99740.99810.99861.00001.96附表2-2标准正态分布表z0.000.010.020.030附表4-1=0.250.100.050.0250.010.005123456789101112131415161.3232.7734.1085.3856.6267.8419.03710.21911.38912.54913.70114.84515.98417.11718.24519.3692.7064.6056.2517.7799.23610.64512.01713.36214.68415.98717.27518.54919.81220.06422.30723.5423.8415.9917.8159.48811.07112.59214.06715.50716.91918.30719.67521.02622.36223.68524.99626.2965.0247.3789.34811.14312.83314.44916.01317.53519.02320.48321.92023.33724.73626.11927.48828.8456.6359.21011.34513.27715.08616.81218.47520.09021.66623.20924.72526.21727.68829.14130.57832.0007.87910.59712.83814.86016.75018.54820.27821.95523.58925.18826.75728.29929.89131.31932.80134.267分布表17.535附表4-1=0.250.100.050.0250.010.=0.9950.990.9750.950.900.75123456789101112131415160.0100.0720.2070.4120.6760.9891.3441.7352.1562.6033.0743.5654.0754.6015.1420.0200.1150.2970.5540.8721.2391.6462.0882.5583.0533.5714.1074.6605.2295.8120.0010.0510.2160.4840.8311.2371.6902.1802.7003.2473.8164.4045.0095.6296.2626.9080.0040.1030.3520.7111.1451.6352.1672.7333.3253.9404.5755.2265.8926.5717.2617.9620.0160.2110.5841.0641.6102.2042.8333.4904.1684.8655.5786.3047.0427.7908.5479.3120.1020.5751.2131.9232.6753.4554.2555.0715.8996.7377.5848.4389.29910.16511.03711.9123.247附表4-2分布表=0.9950.990.9750.950.900.7510.=0.250.100.050.0250.010.0051718192021222324252627282930313220.48921.60522.71823.82824.93526.03927.14128.24129.33930.43531.52832.62033.71134.80035.88736.97324.76925.98927.20428.41229.61530.81332.00733.19634.38235.56336.74137.91639.08740.25641.42242.58527.58728.86930.14431.41032.67133.92435.17236.41537.65238.88540.11341.33742.55743.77344.98546.19430.19131.52632.85234.17035.47936.78138.07639.36440.64641.92343.19444.46145.71246.97948.23249.48033.40934.80536.19137.56638.93240.28941.63842.98044.31445.64246.96348.27849.58850.89252.19153.48635.71837.15638.58239.99741.40142.79644.18145.55946.92848.29049.64550.99352.33653.67255.00356.32834.382附表4-3分布表=0.250.100.050.0250.010.005172附表3-1=0.250.100.050.0250.010.005123456789101112131415161.00000.81650.76490.74070.72670.71760.71110.70640.70270.69980.69740.69550.69380.69240.69120.69013.07771.88561.63771.53321.47591.43981.41491.39681.38301.37221.36341.35621.35021.34501.34061.33686.31382.92002.35342.13182.01501.94321.89461.85951.83311.81251.79591.78231.77091.76131.75311.745912.70624.30273.18242.77642.57062.44692.36462.30602.26222.22812.20102.17882.16042.14482.13152.119931.82076.96464.54073.74693.36493.14272.99802.89652.82142.76382.71812.68102.65032.62452.60252.583563.65749.92485.84094.60414.03223.70743.49953.35543.24983.16933.10583.05453.01232.97682.94672.9208分布表1.8125附表3-1=0.250.100.050.0250.010.附表3-2=0.250.100.050.0250.010.005123456789101112131415161.00000.81650.76490.74070.72670.71760.71110.70640.70270.69980.69740.69550.69380.69240.69120.69013.07771.88561.63771.53321.47591.43981.41491.39681.38301.37221.36341.35621.35021.34501.34061.33686.31382.92002.35342.13182.01501.94321.89461.85951.83311.81251.79591.78231.77091.76131.75311.745912.70624.30273.18242.77642.57062.44692.36462.30602.26222.22812.20102.17882.16042.14482.13152.119931.82076.96464.54073.74693.36493.14272.99802.89652.82142.76382.71812.68102.65032.62452.60252.583563.65749.92485.84094.60414.03223.70743.49953.35543.24983.16933.10583.05453.01232.97682.94672.92082.1315分布表附表3-2=0.250.100.050.0250.010.附表5-1分布表

1234567891012152024304012012345678910111213141516171819647.838.5117.4412.2210.018.818.077.577.216.946.726.556.416.306.206.126.045.955.92799.539.0016.0410.658.437.266.546.065.715.465.265.104.974.864.774.694.624.564.51864.239.1715.449.987.766.605.895.425.084.834.634.474.354.244.154.084.013.953.90899.639.2515.109.607.396.235.525.504.724.474.284.124.003.893.803.733.663.613.56921.839.3014.889.367.155.995.294.824.484.244.043.893.773.663.583.503.443.383.33937.139.3314.739.206.985.825.124.654.234.073.883.733.603.503.413.343.283.223.17948.239.3614.629.076.855.704.994.534.203.953.763.613.483.383.293.223.163.103.05956.739.3714.548.986.765.604.904.434.103.853.663.513.393.293.203.123.063.012.96963.339.3914.478.906.685.524.824.364.033.783.593.443.313.213.123.052.982.932.88968.639.4014.428.846.625.464.764.303.963.723.533.373.253.153.062.992.922.872.82976.739.4114.348.756.525.374.674.203.873.623.433.283.153.052.962.892.822.772.72984.939.4314.258.666.435.274.574.103.773.523.333.183.052.952.862.792.722.672.62993.139.4514.178.566.335.174.474.003.673.423.233.072.952.842.762.682.622.562.51997.239.4614.128.516.285.124.423.593.613.373.173.022.892.792.702.632.562.502.45100139.4614.088.466.235.074.363.893.563.313.122.962.842.732.642.572.502.442.39100639.4714.048.416.185.014.313.843.513.263.062.912.782.672.592.512.442.382.33101439.4913.958.316.074.904.203.733.393.142.942.792.662.552.462.382.322.262.20101839.5013.908.266.024.854.143.673.333.082.882.722.602.492.402.32