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1、会计学1统计数学应用统计数学应用7.1 概率论与数理统计概述概率论与数理统计概述n n7.1.1 离散函数和连续函数n n离散函数：变量是离散变量的函数离散函数：变量是离散变量的函数n n伯努利分布，二项分布，泊松分布伯努利分布，二项分布，泊松分布n n离散变量：其数值只能用自然数或离散变量：其数值只能用自然数或整数单位计算的变量整数单位计算的变量n n人数，交通量，交通密度人数，交通量，交通密度n n连续函数：变量是连续变量的函数连续函数：变量是连续变量的函数n n正态分布，指数分布，正态分布，指数分布，22分布分布分布分布 n n连续变量：在一定区间内可以任意连续变量：在一定区间内可以任意
2、取值的变量取值的变量n n身高，速度，车头时距，车头间距身高，速度，车头时距，车头间距第1页/共25页n n7.1.2 随机性和随机性分布n n随机性：具有某一概率的事件集合中的各个事随机性：具有某一概率的事件集合中的各个事件所表现出来的不确定性件所表现出来的不确定性n n确定性（确定性（实例见实例见P170P170：If you add mass to a If you add mass to a spring or a force to a beam,you can expect it spring or a force to a beam,you can expect it to def
3、lect a predictable amountto deflect a predictable amount）第2页/共25页n n解决随机性问题的基本思想：n nmake things as simple as possible,but no make things as simple as possible,but no simplersimplern n实例：实例：Consider the question of who turns Consider the question of who turns north and who turns south after crossing
4、a north and who turns south after crossing a bridge.Most of the time,we simply say there bridge.Most of the time,we simply say there is a probability p that a vehicle will turn north,is a probability p that a vehicle will turn north,and we treat the outcome as a random and we treat the outcome as a
5、random event.(P170)event.(P170)第3页/共25页n n7.1.3 数据组织n n分组分组n n频率直方图频率直方图n n频率分布图频率分布图n n累积频率分布图累积频率分布图第4页/共25页第5页/共25页第6页/共25页第7页/共25页n n7.1.4 常用估计值n n表示集中程度的估计值表示集中程度的估计值n n算术平均值算术平均值n n中值中值n n众数众数n n表示分散程度的估计值表示分散程度的估计值n n方差方差n n标准差标准差n n协方差协方差第8页/共25页n n算术平均值第9页/共25页n n计算算术平均值的实例1：n nConsider the
6、 following example:Estimate the Consider the following example:Estimate the mean from the following sample speeds in mean from the following sample speeds in mdh:(53,41,63,mdh:(53,41,63,52,41,39,55,34)52,41,39,55,34)（P171P171）第10页/共25页n n计算算术平均值的实例2：n nFor the height data above of Table For the heig
7、ht data above of Table 7.2:(P172)7.2:(P172)第11页/共25页n n计算算术平均值的实例计算算术平均值的实例3 3：n n在某条公路上在某条公路上,上午高峰期间上午高峰期间,以以15s15s为间隔观测到达的车辆数为间隔观测到达的车辆数,结结果如表所示，试求样本均值果如表所示，试求样本均值.车辆到达数车辆到达数k kj j3 33 34 45 56 67 78 89 91010111112121212包含包含k kj j的间隔的间隔出现次数出现次数0 03 30 08 810101111101011119 91 11 10 0第12页/共25页n n中值
8、n n在一组数据中居于中间的数在一组数据中居于中间的数n nFor nongrouped data,it is the middle value;For nongrouped data,it is the middle value;for example,for the set of numbers(3,4,for example,for the set of numbers(3,4,5,5,5,5,6,7,7,7,8),the median is 6.It is the fifth 6,7,7,7,8),the median is 6.It is the fifth value(in asc
9、endmg or descending order)in value(in ascendmg or descending order)in an array of 9 numbers.an array of 9 numbers.n nFor grouped data,the easiest way to get the For grouped data,the easiest way to get the median is to read the 50%percentile point off median is to read the 50%percentile point off a c
10、umulative frequency distribution curvea cumulative frequency distribution curve第13页/共25页n n众数n n一组数据中出现次数最多的数值一组数据中出现次数最多的数值n nFor example,in nongrouped data,for the set For example,in nongrouped data,for the set of numbers(3,4,5,5,6,7,7,7,8),the mode is 7.of numbers(3,4,5,5,6,7,7,7,8),the mode is 7
11、.For the set of numbers(3,3,4,5,5,For the set of numbers(3,3,4,5,5,5,5,6,7,8,6,7,8,8,8,9),both 8,8,9),both 5 5 and 8 are modes,and the data and 8 are modes,and the data is said to be bimodal.is said to be bimodal.n nFor grouped data,the mode is estimated as For grouped data,the mode is estimated as
12、the peak of the frequency distribution curvethe peak of the frequency distribution curve 第14页/共25页n n方差第15页/共25页n n标准差第16页/共25页n n7.1 7.1 概率论与数理统计概述概率论与数理统计概述n n7.2 7.2 正态分布与应用正态分布与应用n n7.3 7.3 置信区间置信区间n n7.4 7.4 样本数量计算样本数量计算n n7.5 7.5 随机变量求和随机变量求和n n7.6 7.6 二项分布与正态分布二项分布与正态分布n n7.7 7.7 泊松分布泊松分布n n7
13、.8 7.8 假设检验假设检验 Chapter 7 Statistical Applications in Traffic Engineering第17页/共25页7.2 正态分布与应用正态分布与应用第18页/共25页n n7.2.1 标准正态分布n nN N（0 0，1 1）n n概率密度值可查表概率密度值可查表7.37.3（P174P174）第19页/共25页n n任意正态分布与标准正态分布的转换：任意正态分布与标准正态分布的转换：n n图图7.27.2n n例子：例子：Consider the following example:For the spot speed Consider t
14、he following example:For the spot speed distribution of Figure 7.2,x:N55,49,what is the probability that distribution of Figure 7.2,x:N55,49,what is the probability that the next observed speed will be 65 mph or less?(P175)the next observed speed will be 65 mph or less?(P175)第20页/共25页n n7.2.2 正态分布的常
15、用值 第21页/共25页专业词专业词n nSampleSample样本样本n npopulationpopulation总体总体n nBernoulli distributionBernoulli distribution伯努里分布伯努里分布n nbinomial distributionbinomial distribution二项分布二项分布n nPoisson distributionPoisson distribution泊松分布泊松分布n nnormal distributionnormal distribution正态分布正态分布n nexponential distributio
16、nexponential distribution指数分布指数分布n nchi-square distributionchi-square distribution卡方分布卡方分布n nrandomnessrandomness随机随机n nfrequency histogramfrequency histogram频率直方图频率直方图n nfrequency distributionfrequency distribution频数分布频数分布第22页/共25页专业词专业词n ncumulative frequency distributioncumulative frequency distr
17、ibution累积频率分布累积频率分布n narithmetic meanarithmetic mean算术平均值算术平均值n nmedianmediann nmodemode众数众数n nvariancevariance方差方差n nstandard deviationstandard deviation标准差标准差n ntolerancetolerance公差公差第23页/共25页作业作业n n复习：7.1,7.2n n笔译：P1172右栏最后一段（The distribution or the underlying shape of the data is of great interest.Is it normal?Exponential?But the engineer is also interested in anomalies in the shape of the distribution(e.g.,skewness or bimodality).)n n预习：7.3，7.4，7.5，7.6，7.7第24页/共25页