标准正态分布的密度函数

标准 excel标准偏差excel标准偏差函数exl标准差函数国标检验抽样标准表免费下载红头文件格式标准下载 正态分布的密度函数 幻灯片1 正态分布 第二章 第七节 一、标准正态分布的密度函数 二、标准正态分布的概率计算 三、一般正态分布的密度函数 四、正态分布的概率计算 幻灯片2 正态分布的重要性 正态分布是概率论中最重要的分布～ 这可以由 以下情形加以说明: ? 正态分布是自然界及 工程 路基工程安全技术交底工程项目施工成本控制工程量增项单年度零星工程技术标正投影法基本原理 技术中最常见的分布 之一～ 大量的随机现象都是服从或近似服从正态分布的( 可以证明～ 如果一个随机指标受到诸多因素的影响, 但其中任何一个因素都不起决定性作用～ 则该随机指标 一定服从或近似服从正态分布( 这些性质是其它 ? 正态分布有许多良好的性质～ 许多分布所不具备的( ? 正态分布可以作为许多分布的近似分布( 幻灯片3 ,标准正态分布 下面我们介绍一种最重要的正态分布 一、标准正态分布的密度函数 若连续型随机变量X的密度函数为 定义 则称X服从标准正态分布～ 记为 标准正态分布是一种特别重要的 它的密度函数经常被使用～ 分布。 幻灯片4 密度函数的验证 则有 ,2, 根据反常积分的运算有 可以推出 幻灯片5 标准正态分布的密度函数的性质 filing. 3, the safety records should be complete in time, and continues to project completion. 4, project safety production management information system of the Ministry of health planning, implementation, c d improved checking and correction, a total of four volumes. Construction and environmental protection in other security measures, such as the first civilization construction and environmental management objectives and civilized construction objectives of civil strive to obtain "safe and civilized model site of Zhuhai city" title. Environmental management goal 1, noise, dust, wastewater discharge standards; reducing and controlling the generation of solid waste; 2, reduce the impact of noise on the surrounding environment, noise complaints decreased by 20%; 3, reduce the consumption of raw materials and energy, construction raw material usage below the standards set by the State, average savings rate of 1% the following three materials. Section II project the civilization construct management system to establish a sound and civilized construction system, at all levels and all departments effective implementation of responsibility system for civil construction, ensure the goal of civilization. Ordinal system name 1 education system extensively and civilized construction management education, improve the overall construction initiative, ideology, so that workers form a building 若随机变量 ～X的密度函数为 则密度函数的性质为: 的图像称为标准正态,高斯,曲线。 幻灯片6 随机变量 由于 由图像可知～阴影面积为概率值。 对同一长度的区间 ～若这区间越靠近 其对应的曲边梯形面积越大。 标准正态分布的分布规律时“中间多～两头少”. 幻灯片7 二、标准正态分布的概率计算 1、分布函数 分布函数为 幻灯片8 2、标准正态分布表 书 关于书的成语关于读书的排比句社区图书漂流公约怎么写关于读书的小报汉书pdf 末附有标准正态分布函数数值表～有了它～ 可以解决标准正态分布的概率计算. 表中给的是x > 0时, Φ(x)的值. 幻灯片9 如果 由公式得 令 则 幻灯片10 例1 解 幻灯片11 由标准正态分布的查表计算可以求得～ 当X，N(0,1)时～ 这说明～X 的取值几乎全部集中在[-3,3]区间内～ 超出这个范围的可能性仅占不到0.3%. 幻灯片12 三、一般正态分布的密度函数 如果连续型随机变量X的密度函数为 ,其中 为参数, 的正态分布～记为 则随机变量X服从参数为 所确定的曲线叫 作正态(高斯,曲线. 幻灯片13 filing. 3, the safety records should be complete in time, and continues to project completion. 4, project safety production management information system of the Ministry of health planning, implementation, c d improved checking and correction, a total of four volumes. Construction and environmental protection in other security measures, such as the first civilization construction and environmental management objectives and civilized construction objectives of civil strive to obtain "safe and civilized model site of Zhuhai city" title. Environmental management goal 1, noise, dust, wastewater discharge standards; reducing and controlling the generation of solid waste; 2, reduce the impact of noise on the surrounding environment, noise complaints decreased by 20%; 3, reduce the consumption of raw materials and energy, construction raw material usage below the standards set by the State, average savings rate of 1% the following three materials. Section II project the civilization construct management system to establish a sound and civilized construction system, at all levels and all departments effective implementation of responsibility system for civil construction, ensure the goal of civilization. Ordinal system name 1 education system extensively and civilized construction management education, improve the overall construction initiative, ideology, so that workers form a building 一般正态分布密度函数的图形性质 幻灯片14 (4) 幻灯片15 (5) 若σ固定，而改变μ的值， µ称为位置参数。 幻灯片16 (6) 若μ 固定，而改变σ的值， 正态分布由它的两个参数μ和 μ和σ不同时， 当 σ惟一确定， 是不同的正态分布. 幻灯片17 时的 可以认为～ X的取值几乎全部集中在 的区间内。 幻灯片18 四、正态分布的概率计算 设 X 的分布函数是 幻灯片19 任何一个一般的 标准正态分布的重要性在于～ 正态分布都可以通过线性变换转化为标准正态分布. 它的依据是下面的引理: 设 引理 则 根据引理, 只要将标准正态分布的分布函数制成表～ 就可以解决一般正态分布的概率计算问 题 快递公司问题件快递公司问题件货款处理关于圆的周长面积重点题型关于解方程组的题及答案关于南海问题 . 幻灯片20 一般正态分布的计算 若 设 幻灯片21 例3 解 幻灯片22 例3 解 幻灯片23 已知 filing. 3, the safety records should be complete in time, and continues to project completion. 4, project safety production management information system of the Ministry of health planning, implementation, c d improved checking and correction, a total of four volumes. Construction and environmental protection in other security measures, such as the first civilization construction and environmental management objectives and civilized construction objectives of civil strive to obtain "safe and civilized model site of Zhuhai city" title. Environmental management goal 1, noise, dust, wastewater discharge standards; reducing and controlling the generation of solid waste; 2, reduce the impact of noise on the surrounding environment, noise complaints decreased by 20%; 3, reduce the consumption of raw materials and energy, construction raw material usage below the standards set by the State, average savings rate of 1% the following three materials. Section II project the civilization construct management system to establish a sound and civilized construction system, at all levels and all departments effective implementation of responsibility system for civil construction, ensure the goal of civilization. Ordinal system name 1 education system extensively and civilized construction management education, improve the overall construction initiative, ideology, so that workers form a building 例4 求 解 幻灯片24 例5 某地区18至22岁的男子身高为X , 从该地区 1、随机地抽查一青年男子的身高～ 他身高超过168cm 的概率为多少。 2、若抽查10个青年男子测其身高恰有k,0?k ? 10)个 人的身高高于168cm 的概率为多少, 解 1、 2、 设该地区身高高于168cm的人数为X . 幻灯片25 公共汽车车门的高度是按男子与车门顶头碰头机会在0.01以下来设计的.设男子身 高X,N (170,62),问车门高度应如何确定? 例6 解: 设车门高度为h cm,按设计要求 或 因为 X，N(170,62), 故 0.99 查表得 (2.33)=0.9901>0.99 即 设计车门高度为184厘米时～ 可使男子与车门碰头机会不超过0.01. 幻灯片26 例7 解 幻灯片27 一种电子元件的使用寿命,(小时)服从正态分布,(100,152),某仪器上装有3个 这种元件，三个元件损坏与否是相互独立的.求:使用的最初90小时内无一元件损坏的概率. 例8 解: 设Y为使用的最初90小时内损坏的元件数, 则 其中 故 幻灯片28 例9 设某工程队完成某项工程所需时间为X (天)近似 的正态分布。 奖金办法规定: 服从参数为 filing. 3, the safety records should be complete in time, and continues to project completion. 4, project safety production management information system of the Ministry of health planning, implementation, c d improved checking and correction, a total of four volumes. Construction and environmental protection in other security measures, such as the first civilization construction and environmental management objectives and civilized construction objectives of civil strive to obtain "safe and civilized model site of Zhuhai city" title. Environmental management goal 1, noise, dust, wastewater discharge standards; reducing and controlling the generation of solid waste; 2, reduce the impact of noise on the surrounding environment, noise complaints decreased by 20%; 3, reduce the consumption of raw materials and energy, construction raw material usage below the standards set by the State, average savings rate of 1% the following three materials. Section II project the civilization construct management system to establish a sound and civilized construction system, at all levels and all departments effective implementation of responsibility system for civil construction, ensure the goal of civilization. Ordinal system name 1 education system extensively and civilized construction management education, improve the overall construction initiative, ideology, so that workers form a building 若在100天内完成～则得超产奖 10000元, 若在100天至115天内完成～则得超产奖 1000元, 若完成时间超过115天～则罚款 5000元。 求该工程队在完成这项工程时～ 奖金额Y的分布列。 解 依题意 可见Y是X的函数～ 且是离散型随机变量。 幻灯片29 则Y 的分布列 幻灯片30 查表可知 幻灯片31 作业 P142 16 17 18 19 20 幻灯片32 正态分布 在处理实际问题时常常遇到这样一种随机变量～ 对它进行大量重复的观察～ 得到一组数据。 这组数据 虽然有波动～ 但总是以某个常数为中心。 偏离中心 取值呈 偏离中心越远的数据越少。 越近的数据越多, 且取值具有对称性。 “中间大、两头小”的格局～ 如:人体身高、智力、学习成绩、电器寿命等。 产生这种现象的原因是受多因素的影响～ 而每一种因 素在正常情况下都是相互独立的～ 且它们的影响是均匀 的、微小的。 所以人体身高、智力、成绩、寿命为随机 变量是一个服从正态分布的随机变量。 这种随机变量的 密度曲线是单峰的～ 且有左右对称的形状。 filing. 3, the safety records should be complete in time, and continues to project completion. 4, project safety production management information system of the Ministry of health planning, implementation, c d improved checking and correction, a total of four volumes. Construction and environmental protection in other security measures, such as the first civilization construction and environmental management objectives and civilized construction objectives of civil strive to obtain "safe and civilized model site of Zhuhai city" title. Environmental management goal 1, noise, dust, wastewater discharge standards; reducing and controlling the generation of solid waste; 2, reduce the impact of noise on the surrounding environment, noise complaints decreased by 20%; 3, reduce the consumption of raw materials and energy, construction raw material usage below the standards set by the State, average savings rate of 1% the following three materials. Section II project the civilization construct management system to establish a sound and civilized construction system, at all levels and all departments effective implementation of responsibility system for civil construction, ensure the goal of civilization. Ordinal system name 1 education system extensively and civilized construction management education, improve the overall construction initiative, ideology, so that workers form a building