第七章 概率分布(下).pptVIP

Chapter 7b Probability Distributions 第七章 概率分布(下) Chapter 7b Probability Distributions 数据的类型 Data Types 7.4 连续型随机变量的概率分布 Probability Distribution of ContinuousRandom Variables 7.4.1 连续型随机变量 Continuous Random Variable 随机变量 Random Variable 某试验的数量结果 A Numerical Outcome of an Experiment 例如：体重 Weight of a Student (e.g., 115, 156.8, etc.) 连续型随机变量 Continuous Random Variable 整数或分数 Whole or Fractional Number 通过测量获得 Obtained by Measuring 在区间内有无限取值 Infinite Number of Values in Interval 多得无法像离散变量那样列举 Too Many to List Like Discrete Variable 连续型随机变量举例Continuous Random Variable Examples 7.4.2 连续型概率密度函数Continuous Probability Density Function 数学公式 Mathematical Formula 描述随机变量的所有可能值x及其对应的频率f(x) Shows all values, x, frequencies, f(x) f(x) 不是概率而是概率密度 性质 Properties 7.4.3 连续型随机变量的概率Continuous Random Variable Probability 7.4.5 连续型概率分布的数字特征Summary Measures 期望值 Expected Value —— 中心 7.4.6 连续型概率分布模型Continuous Probability Distribution Models 7.5 均匀分布 Uniform Distribution 连续型概率分布模型Continuous Probability Distribution Models 均匀分布 Uniform Distribution 各结果等可能 Equally Likely Outcomes 概率密度函数 Probability Density 均匀分布举例Uniform Distribution Example You’re production manager of a soft drink bottling company. You believe that when a machine is set to dispense 12 oz., it really dispenses 11.5 to 12.5 oz. inclusive. Suppose the amount dispensed has a uniform distribution. What is the probability that less than 11.8 oz. is dispensed? 解答 Uniform Distribution Solution P(11.5 ? x ? 11.8) = (Base)(Height) = (11.8 - 11.5)(1) = 0.30 7.6 正态分布 Normal Distribution 连续型概率分布模型Continuous Probability Distribution Models 7.6.1 正态分布的重要性Importance of Normal Distribution 许多连续型随机变量都服从正态分布 Describes Many Random Processes or Continuous Phenomena 标准化考试成绩、大量生理现象(身高、智商、……) 能用以近似计算离散概率分布 Can Be Used to Approximate Discrete Probability Distributions 如二项分布 Example: Binomial 统计推断的基础 Basis for Classical Statistical Inference 如抽样分布 7.6.2 正态分布概率密度函数 Probability Density Function f(x) = 随机变量x的频率 Frequency of Random Variab