概率论与数理统计电子教案（配浙大第四版）6.3 抽样分布.ppt

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1、第三节抽样分布一、基本概念二、常见分布三、小结一、基本概念1.统计量的定义是不是实例12.几个常用统计量的定义(1)样本平均值(2)样本方差其观察值其观察值(3)样本标准差其观察值(4)样本k阶(原点)矩其观察值(5)样本k阶中心矩其观察值证明再根据第五章辛钦定理知由以上定义得下述结论:辛钦定理由第五章关于依概率收敛的序列的性质知以上结论是下一章所要介绍的矩估计法的理论根据.3.经验分布函数经验分布函数的做法如下:实例实例一般地，格里汶科定理格里汶科资料二、常见分布统计量的分布称为抽样分布.自由度

2、是指上式右端包含的独立变量的个数.证明性质1(此性质可以推广到多个随机变量的情形.)性质2证明根据正态分布的对称性知例1附表1-1附表1-2课本附表5只详列到n=40为止.例2在Matlab中求解附表2-1附表2-2附表2-3例如利用上面公式,而查详表可得费希尔(R.A.Fisher)证明:费希尔资料t分布又称学生氏(Student)分布.2.随机数演示分布函数与密度函数演示学生氏资料形.当n充分大时,其图形类似于标准正态变量概率密度的图由分布的对称性知例3在Matlab中求解附表3-1附表3-2

3、3.随机数演示分布函数与密度函数演示根据定义可知,例4在Matlab中求解附表4-2附表4-1证明4.正态总体的样本均值与样本方差的分布定理一定理二证明由t分布的定义知定理三且两者独立,定理四证明(1)由定理二(2)三、小结两个最重要的统计量:样本均值样本方差三个来自正态分布的抽样分布:辛钦定理返回附表1-1标准正态分布表z01234567890.00.10.20.30.40.50.60.70.80.91.01.11.21.31.41.51.60.50000.53980.57930.61790.6

4、5540.69150.72570.75800.78810.81590.84130.86430.88490.90320.91920.93320.94520.50400.54380.58320.62170.65910.69500.72910.76110.79100.81860.84380.86650.88690.90490.92070.93450.94630.50800.54780.58710.62550.66280.69850.73240.76420.79390.82120.84610.86860.

5、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

6、.63680.67360.70880.74220.77340.80230.82890.85310.87490.89440.91150.92650.93940.95050.52390.56360.60260.64060.67720.71230.74540.77640.80510.83150.85540.87700.89620.91310.92780.94060.95150.52790.56750.60640.64430.68080.71570.74860.77940.80780.83400.8577

7、0.87900.89800.91470.92920.94180.95250.53190.57140.61030.64800.68440.71900.75170.78230.81060.83650.85990.88100.89970.91620.93060.94300.95350.53590.57530.61410.65170.68790.72240.75490.78520.81330.83890.86210.88300.90150.91770.93190.94410.95451.645返回附表1-

8、2标准正态分布表z01234567891.61.71.81.92.02.12.22.32.42.52.62.72.82.93.00.94520.95540.96410.97130.97720.98210.98610.98930.99180.99380.99530.99650.99740.99810.99870.94630.95640.96480.97190.97780.98260.98640.98960.99200.99400.99550.99660.99750.99820.999