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1、高中数学概率统计知识点总结高中数学概率统计知识点总结 一、抽样方法 1(简单随机抽样 2(简单随机抽样常用的方法:(1)抽签法;?随机数表法。 3(系统抽样:K(抽样距离)=N(总体规模)/n(样本规模) 4(分层抽样: 二、样本估计总体的方式 1、用样本的频率分布估计总体分布 (1)频率分布直方图的画法;(2)频率的算法;(3)频率分布折线图;(4)总体密度曲线;(5)茎叶图。 茎叶图又称“枝叶图”，它的思路是将数组中的数按位数进行比较，将数的大小基本不变或变化不大的位作为一个主干(茎)，将变化大的位的数作为分枝(叶)，列在主干的后面，这样就可以清楚地看到每个主干后面的几个数，每个数具体是多
2、少。 2、用样本的数字特征估计总体的数字特征 (1)众数、中位数、平均数的算法;(2)标准差、方差公式。 xxx，？，12nx,3、样本均值: n222xxxxxx(,)，(,)，？，(,)212nss4、(样本标准差: ,n三、两个变量的线性相关 1、正相关2、负相关 正相关:自变量增加，因变量也同时增加(即单调递增) 负相关:自变量增长，因变量减少(即单调递减) 四、概率的基本概念 (1)必然事件(2)不可能事件(3)确定事件(4)随机事件 (5)频数与频率(6)频率与概率的区别与联系 必然事件和不可能事件统称为确定事件 1他们都是统计系统各元件发生的可能性大小; 2、频率一般是大概统计数
3、据经验值，概率是系统固有的准确值; 3频率是近似值，概率是准确值 the first level to consider when positioning security, roughly the same distance between the point and level to put the stand, cant be moved, dislocation, and so on. Pay attention to the proper use and care of leveling. (6) level: find the anchor position after take
4、levels, in anchor horizontal, horizontal lines with fine steel wire cable, while tightly tightening, ensure the wire level. (7) measurement errors: in horizontal line after the measure on the face. Mainly for horizontal measurement, also check the axis (axis positioning) q errors. By measuring the r
5、esults of analyzing the cause of error, check the relevant specification (construction) requirements for error values, within the specified error, digestible errors exceeded error shall be settled through consultation with civil party or party. (8) to adjust the error: . (3) familiar with their loca
6、tion and adjacent location, check the accuracy of segment size. (4) attention to handling errors, strengthen coordination with civil engineering work. (5) check the embedded location is accurate, solid reinforcement. 7. Security, protection: (1) enter the construction site personnel must wear safety
7、 helmets, safety belts, shirtless, wearing slippers, slippery-soled shoes is not allowed to enter the site. (2) must be carried out according to the specifications of construction, attention to the safe use of electricity. (3) Note 4、频率值一般容易得到，所以一般用来代替概率 进行定量分析，首先要知道系统各元件发生故障的频率或概率。 事件的频率与概率是度量事件出现可
8、能性大小的两个统计特征数。 频率是个试验值，或使用时的统计值，具有随机性，可能取多个数值。因此，只能近似地反映事件出现可能性的大小 概率是个理论值，是由事件的本质所决定的，只能取唯一值，它能精确地反映事件出现可能性的大小 虽然概率能精确反映事件出现可能性的大小，但它通过大量试验才能得到，这在实际工作中往往是难以做到的。所以，从应用角度来看，频率比概率更有用，它可以从所积累的比较多的统计资料中得到 需要指出的是用频率代替概率，并不否认概率能更精确、更全面地反映事件出现可能性的大小，只是由于在目前的条件下，取得概率比取得频率更为困难。 所以，我们才用频率代替概率，以概率的计算方法来计算频率 五、
9、概率的基本性质 1、基本概念:(1)事件的包含并事件、交事件、相等事件 (2)若A?B为不可能事件，即A?B=，那么称事件A与事件B互斥; ,(3)若A?B为不可能事件，A?B为必然事件，那么称事件A与事件B互为对 立事件; (4)当事件A与B互斥时，满足加法公式:P(A?B)= P(A)+ P(B); 若事件A与B为对立事件，则A?B为必然事件，所以P(A?B)= P(A)+ P(B)=1， 于是有P(A)=1P(B)。 2、概率的基本性质: (1)必然事件概率为1，不可能事件概率为0，因此0?P(A)?1; the first level to consider when position
10、ing security, roughly the same distance between the point and level to put the stand, cant be moved, dislocation, and so on. Pay attention to the proper use and care of leveling. (6) level: find the anchor position after take levels, in anchor horizontal, horizontal lines with fine steel wire cable,
11、 while tightly tightening, ensure the wire level. (7) measurement errors: in horizontal line after the measure on the face. Mainly for horizontal measurement, also check the axis (axis positioning) q errors. By measuring the results of analyzing the cause of error, check the relevant specification (
12、construction) requirements for error values, within the specified error, digestible errors exceeded error shall be settled through consultation with civil party or party. (8) to adjust the error: . (3) familiar with their location and adjacent location, check the accuracy of segment size. (4) attent
13、ion to handling errors, strengthen coordination with civil engineering work. (5) check the embedded location is accurate, solid reinforcement. 7. Security, protection: (1) enter the construction site personnel must wear safety helmets, safety belts, shirtless, wearing slippers, slippery-soled shoes
14、is not allowed to enter the site. (2) must be carried out according to the specifications of construction, attention to the safe use of electricity. (3) Note (2)当事件A与B互斥时，满足加法公式:P(A?B)= P(A)+ P(B); (3)若事件A与B为对立事件，则A?B为必然事件，所以P(A?B)= P(A)+ P(B)=1，于是有P(A)=1P(B); (2)两锐角的关系：AB=90；(4)互斥事件与对立事件的区别与联系，互斥事件
15、是指事件A与事件B在一次试验中不会同时发生，其具体包括三种不同的情形: (1)事件A发生且事件B不发生; (2)事件A不发生且事件B发生; (3)事件A与事件B同时不发生，而对立事件是指事件A 与事件B有且仅有一个发生，其包括两种情形;(1)事件A发生B不发生;(2)事件B发生事件A不发生，对立事件互斥事件的特殊情形。 六、古典概型 1、(1)古典概型的使用条件:试验结果的有限性和所有结果的等可能性。 (2)古典概型的解题步骤; cos?求出总的基本事件数; 上述五个条件中的任何两个条件都可推出其他三个结论。?求出事件A所包含的基本事件数，然后利用公式 弧、半圆、优弧、劣弧：弧：圆上任意两点间
16、的部分叫做圆弧，简称弧，用符号“”表示，以CD为端点的弧记为“”，读作“圆弧CD”或“弧CD”。半圆：直径的两个端点分圆成两条弧，每一条弧叫做半圆。优弧：大于半圆的弧叫做优弧。劣弧：小于半圆的弧叫做劣弧。(为了区别优弧和劣弧，优弧用三个字母表示。)A包含的基本事件数P(A)= 总的基本事件个数七、几何概型 10.三角函数的应用1、基本概念: (1)几何概率模型:如果每个事件发生的概率只与构成该事件区域的长度(面积或体积)成比例，则称这样的概率模型为几何概率模型; (2)几何概型的概率公式: 圆由两个条件唯一确定：一是圆心（即定点），二是半径（即定长）。构成事件A的区域长度(面积或体积)P(A)
17、= ; 试验的全部结果所构成的区域长度(面积或体积)115.75.13加与减（二）2 P61-63 数学好玩2 P64-67(3)几何概型的特点: B、当a0时1)试验中所有可能出现的结果(基本事件)有无限多个; （2）交点式：y=a(x-x1)(x-x2)2)每个基本事件出现的可能性相等( 1、会数、会读、会写100以内的数;在具体情境中把握数的相对大小关系;能够运用数进行表达和交流，体会数与日常生活的密切联系。the first level to consider when positioning security, roughly the same distance between th
18、e point and level to put the stand, cant be moved, dislocation, and so on. Pay attention to the proper use and care of leveling. (6) level: find the anchor position after take levels, in anchor horizontal, horizontal lines with fine steel wire cable, while tightly tightening, ensure the wire level.
19、(7) measurement errors: in horizontal line after the measure on the face. Mainly for horizontal measurement, also check the axis (axis positioning) q errors. By measuring the results of analyzing the cause of error, check the relevant specification (construction) requirements for error values, withi
20、n the specified error, digestible errors exceeded error shall be settled through consultation with civil party or party. (8) to adjust the error: . (3) familiar with their location and adjacent location, check the accuracy of segment size. (4) attention to handling errors, strengthen coordination wi
21、th civil engineering work. (5) check the embedded location is accurate, solid reinforcement. 7. Security, protection: (1) enter the construction site personnel must wear safety helmets, safety belts, shirtless, wearing slippers, slippery-soled shoes is not allowed to enter the site. (2) must be carried out according to the specifications of construction, attention to the safe use of electricity. (3) Note