第3节-常用统计分布(三个常用分布).ppt

第3节抽样分布一、常见分布二、概率分布的分位数三、小结

一、常见分布

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

注自由度减少一个!减少一个自由度的原因：事实上，它们受到一个条件的约束：

同理与相互独立

t分布又称学生氏(Student)分布.3.

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

定理总体X和Y，则

证由定理知

例3解

4.其中分别表示F分布的自由度

(1)

二、概率分布的分位数ax记x为xa

附表2-1根据正态分布的对称性知附表2-2

由分布的对称性知

附表3-1附表3-2

附表4-1附表4只详列到n=45为止.附表4-2附表4-3

例如利用上公式,而查详表可得费歇(R.A.Fisher)证明:

附表5-1附表5-2

证明

三、小结1.三大统计分布的定义,性质.2.概率分布的分位数

练习

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2-2标准正态分布表z0.000.010.020.030.040.050.060.070.080.091.61.71.81.92.02.12.22.32.42.52.62.72.82.93.00.94520.95540.96410.97130.97720.98210.98610.98930.99180.99380.99530.99650.99740.99810.99870.94630.95640.96480.97190.97780.98260.98640.98960.99200.99400.99550.99660.99750.99820.99900.94740.95730.96560.97260.97830.98300.98680.98980.99220.99410.99560.99670.99760.99820.99930.94840.95820.96640.97320.97880.98340.98710.99010.99250.99430.99570.99680.99770.99830.99950.94950.95910.9