西南交通大学：《管理统计学》（双语版） 第2章 概率分布

第2章概率分布 Normal Distrib .Other Continuous Distributions

第2章 概率分布 •Normal Distribution •Other Continuous Distributions

本章概要 The Normal distribution The Standard Normal distribution . Assessing the Normality Assumption The Exponential Distribution .Sampling Distribution of the Mean Sampling Distribution of the Proportion Sampling from Finite populations

本章概要 •The Normal Distribution •The Standard Normal Distribution •Assessing the Normality Assumption •The Exponential Distribution •Sampling Distribution of the Mean •Sampling Distribution of the Proportion •Sampling From Finite Populations

Continuous Probability Distributions 连续的概率分布 Continuous Random variable Values from Interval of Numbers Continuous Probability Distribution: Distribution of a Continuous Variable .Most Important Continuous Probability Distribution the Normal Distribution

Continuous Probability Distributions 连续的概率分布 •Continuous Random Variable: Values from Interval of Numbers Continuous Probability Distribution: Distribution of a Continuous Variable •Most Important Continuous Probability Distribution: the Normal Distribution

The normal distribution 正态分布 Bell Shaped Symmetrical f(X) Mean Median and Mode are Equal X Middle Spread? Mean Equals1.33σ Median Random variable has Mode Infinite Range

The Normal Distribution 正态分布 • Bell Shaped • Symmetrical • Mean, Median and Mode are Equal • Middle Spread? Equals 1.33  • Random Variable has Infinite Range Mean Median Mode X f(X) 

概率密度函数 (Probability Density Function, p.d.f.) 1(-1/2)(x-po 2no fX)- frequency of random variable X 3.14159;e=2.71828 population standard deviation value of random variable (-o0< X<oo) population mean 总体均数)

概率密度函数 (Probability Density Function, p.d.f. ) f(X) = frequency of random variable X  = 3.14159; e = 2.71828  = population standard deviation X = value of random variable (- < X < )  = population mean (总体均数) f(X) = 1 e (-1/2)((X- )) 2 2

多个正态分布的比较 There are an Infinite Number Varying the parameters o and u, we obtain Different Normal Distributions

多个正态分布的比较 Varying the Parameters  and , we obtain Different Normal Distributions. There are an Infinite Number

Normal Distribution: Finding probabilities 正态分布曲线下面积的几何意义 Probability is the area under the curve!累积概率 P(c≤X≤d)=? f(X X cd

Normal Distribution: Finding Probabilities 正态分布曲线下面积的几何意义 Probability is the area under the curve ! 累积概率 c d X f(X) P (c  X  d )= ?

每个正态分布对应一张正态概率表 Which table?请用标准正态分布! Each distribution has its own table? Infinitely Many Normal Distributions Means Infinitely Many Tables to Look Ur

每个正态分布对应一张正态概率表 Which Table? 请用标准正态分布！ Infinitely Many Normal Distributions Means Infinitely Many Tables to Look Up! Each distribution has its own table?

The standardized normal distribution 标准正态分布 Standardized Normal Probability Table(portion) u,0 and o=2 0478 Z.00.01 0.0.0000.0040.0080 0398.0438.0478 0.2.0793.0832.0871 乙=0.12 0.3.0179.0217.0255 Shaded Area Probabilities Exaggerated

Z Z Z = 0.12 Z .00 .01 0.0 .0000 .0040 .0080 .0398 .0438 0.2 .0793 .0832 .0871 0.3 .0179 .0217 .0255 The Standardized Normal Distribution 标准正态分布 .0478 .02 0.1 .0478 Standardized Normal Probability Table (Portion)  = 0 and  = 1 Probabilities Shaded Area Exaggerated

标准化的应用(1) 2X-=6.2-5 0.12 10 Normal Standardized Normal Distribution Distribution G=10 H=56.2X H=0.12z Shaded Area Exaggerated

 = 0 Z Z = 1 .12 标准化的应用（1） Normal Distribution Standardized Normal Distribution  = 5 X  = 10 6.2 0 12 10 6 2 5 . X . Z = − = − =   Shaded Area Exaggerated