江苏自考27173工程数学复习资料

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relationship, established equivalent relationship 14, and subject: application problem (4)--scores and percentage application problem review content overview answers scores, and percentage application problem of key is: according to meaning, (1) determine standard volume (units \onship, Then inbinati-line solution. Category fraction multiplication word problem score Division applications engineering problem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurnd ement of common units of measurement and their significance in rate 1, currency, length, area, volume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units and their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and tool measurement 2, and estimates 16, and subject: geometry preliminary knowledge (1)--line and angle review content line, and segment, and Ray, and vertical, and parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)--plane graphics review content triangle, and edges shaped, and round, and fan axisymmetric graphics perimeter and area comon graphics of area subject : Preliminary knowledge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided into: cuboid, square 3, cone cone of the features of cuboids acubes relationship between characteristics of circular cone is slightly solid surface area and volume 1, size 2, table ...和第一章随机事件与随机事件的概率

本章考核内容小结

（一）了解随机事件的概率的概念，会用古典概型的计算公式

计算简单的古典概型的概率（不返回抽样、返回抽样）（二）知道事件的四种关系

（1）包含：表示事件A发生则事件B必发生

（2）相等：

（3）互不相容：与B互不相容（4）对立：A与B对立AB=Φ，且A+B=Ω （三）知道事件的四种运算

（1）事件的和（并）A+B表示A与B中至少有一个发生性质：（1）若，则A+B=A（2）（2）事件积（交）AB表示A与B都发生

性质：（1）若（2）

且

，则AB=B，A+B=A ∴ΩB=B且

（3）事件的差：A-B表示A发生且B不发生 ∴（4）性质

表示A不发生

，且A-B=A-AB

（四）运算关系的规律

（1）A+B=B+A，AB=BA叫交换律（2）（A+B）+C=A+（B+C）（AB）C=A（BC）叫结合律（3）A（B+C）=AB+AC （A+B）（A+C）=A+BC叫分配律

（4）

叫对偶律

（五）掌握概率的计算公式

（1）P（A+B）=P（A）+P（B）-P（AB）

特别情形①A与B互斥时：P（A+B）=P（A）+P（B）

②A与B独立时：P（A+B）=P（A）+P（B）-P（A）P（B）

③

推广P（A+B+C）=P（A）+P（B）+P（C）-P（AB）-P（AC）-P（BC）+P（ABC）

（2）

推广：

relationship, established equivalent relationship 14, and subject: application problem (4)--scores and percentage application problem review content overview answers scores, and percentage application problem of key is: according to meaningolume (units \onship, Then in-line solution. Category fraction multiplication word problem score Division applications engineering problem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurnd ement of common units of measurement and their significance in rate 1, currency, length, area, volume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units and their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and tool measurement 2, and estimates 16, and subject: geometry preliminary knowledge (1)--line and angle review content line, and segment, and Ray, and vertical, and parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)--plane graphi, (1) determine standard vcs review content triangle, and edges shaped, and round, and fan axisymmetric graphics perimeter and area combination graphics of area subject : Preliminary knowledge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided into: cuboid, square 3, cone cone of the features of cuboids acubes relationship between characteristics of circular cone is slightly solid surface area and volume 1, size 2, table ...和当事件独立时，P（AB）=P（A）P（B） P（ABC）=P（A）P（B）P（C）

P（ABCD）=P（A）P（B）P（C）P（D）性质若A与B独立

与B，A与

，

与

均独立

（六）熟记全概率公式的条件和结论

若A1，A2，A3是Ω的划分，则有

简单情形

熟记贝叶斯公式

若已知，则

（七）熟记贝努利重复试验概型的计算公式

第二章随机变量及其变量分布

（一）知道随机变量的概念，会用分布函数求概率

（1）若X是离散型随机变量，则P（a

P（a≤x≤b）=F（b）- F（a） P（a≤x＜b）=F（b）- F（a） P（a

会求简单离散型随机变量的分布律和分布函数，且若

则

（三）掌握三种常用的离散型随机变量的分布律（1）X～（0,1）（2）X～B（n,p）

P（x=k）=

（3）X～P（λ）P（x=k）=

（四）知道连续型随机变量的概率密度概念和性质，概率密度和分布函数的关系及由概率密度求概率的公式。

relationship, established equivalent relationship 14, and subject: application problem (4)--scores and percentage application problem review content overview answers scores, and percentage application problem of key is: according to meaningolume (units \orresponds to\onship, Then in-line solution. Category fraction multiplication word problem score Division applications engineering problem problem XV, a subject: review of the measurement pacity, measurement and units of measurement of common units of measurement and their significance in rate 1, currency, length, area, volume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units and their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and tool measurement 2, and estimates 16, and subject: geometry preliminary knowledge (1)--line and angle review content line, and segment, and Ray, and vertical, and parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)--plane graphi, (1) determine standard vcs review content triangle, and edges shaped, and round, and fan axisymmetric graphics perimeter and area combination graphics of area subject : Preliminary knowledge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided iof the amount of canto: cuboid, square 3, cone cone of the features of cuboids and cubes relationship between characteristics of circular cone is slightly solid surface area and volume 1, size 2, table ...和（1）概率密度f（x）的性质 ①f（x）≥0 ②

（2）分布函数和概率密度的关系

（3）分布函数的性质①F（x）右连续 ②F（－∞）＝0，F（+∞）＝1 ③F（x）是不减函数。（4）概率计算公式：①P（a

（1）X～U（a,b） X～f（x）= X～F（x）=

（2）X～E（λ）①X～f（x）=②X～F（x）=

（3）X～N（0,1）①X～②X～

性质：Φ（-x）=1-Φ（x） P（a

（4）X～N（μ,σ2）①X～②P（a

（1）离散型

若

且g（x1）,g（x2）, …g（xn）不相同时，有

*（2）连续型

若X～fX（x）,y=g（x）单调，有反函数x=h（y）且y的取值范围为（α,β），则随机变

量X的函数Y=g（x）的概率密度为

当α=－∞β=+∞时，则有

简单情形，若Y＝ax+b则有Y～fY（y）= 在简单情形下会用公式法求Y＝ax+b的概率密度。（3）重要结论

（i）若X～N（μ,σ2），则有Y＝ax+b时Y～N（aμ+b,a2σ2）

（ii）若X～N（μ,σ2），则有Y＝

叫X的标准化随机变量。

第三章多维随机变量及概率分布

（一）知道二维随机变量的分布函数的概念和性质。（1）（X，Y）～F（X,Y）=P（X≤X,Y≤Y）=P（-∞＜X≤X, -∞＜Y≤Y）（2）F（X,Y）的性质

（ⅰ）F（+∞，+∞）=1 （ⅱ）F（-∞，Y）=0，F（X，-∞）=0 F（-∞，-∞）=0

relationship, established equivalent relationship 14, and subject: application problem (4)--scores and percentage application problem review content overview answers scores, and percentage application problem of key is: according to meaningolume (units \onship, Then in-line solution. Category fraction multiplication word problem score Division applications engineering problem problem XV, a subject: review of the measurement of the amount of capacity, measurement and units of measurnd ement of common units of measurement and their significance in rate 1, currency, length, area, volume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units and their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and tool measurement 2, and estimates 16, and subject: geometry preliminary knowledge (1)--line and angle review content line, and segment, and Ray, and vertical, and parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)--plane graphi, (1) determine standard vcs review content triangle, and edges shaped, and round, and fan axisymmetric graphics perimeter and area combination graphics of area subject : Preliminary knowledge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided into: cuboid, square 3, cone cone of the features of cuboids acubes relationship between characteristics of circular cone is slightly solid surface area and volume 1, size 2, table ...和（3）X～FX（X）=F（X,+ ∞） Y～FY（Y）=F（+∞,Y）

（二）离散型二维随机变量（1）（X，Y）的分布律

（2）X的边缘分布

性质

证明 P1·=P11+P12+…P1N， P2·=P21+P22+…P2N，… pm·=pm1+pm2+…pmn （3）Y的分布律

证 P·1=P11+P21+…pm1， P·2=P21+P22+…pm2，… P·N= P1N+P2N+…+pmn （4）X，Y独立的充要条件是：

X，Y独立P（X=xi,Y=yj）=P（X=xi）P（Y=yj）（i=1,2,…,M；j=1,2,…,N）判断离散性随机变量X，Y是否独立。（5）会求 Z=X+Y的分布律（三）二维连续型随机变量

（1）若

已知 f（X,Y）时，会用上式求F（X,Y）性质（2）（3）会用公式

已知F（X,Y）时，会用上式求f（X,Y）

求（X，Y）在区域D上取值的概率。

（4）会用公式分别求X，Y的概率密度（边缘密度）（5）会根据X，Y独立判断连续型随机变量X，Y的独立性。（6）知道两个重要的二维连续随机变量

①（X，Y）在D上服从均匀分布

则X，Y独立

（7）若X，Y独立，且

S是D的面积

第四章随机变量的数字特征

relationship, established equivalent relationship 14, and subject: application problem (4)--scores and percentage application problem review content overview answers scores, and percentage application problem of key is: according to meaningolume (units \orresponds to\onship, Then in-line solution. Category fraction multiplication word problem score Division applications engineering problem problem XV, a subject: review of the measurement pacity, measurement and units of measurement of common units of measurement and their significance in rate 1, currency, length, area, volume, unit size, volume, weight and rate. (Omitted) 2, commonly used time units and their relationships. (Slightly) with a measurement units Zhijian of of poly 1, and of method 2, and poly method 3, and of method and poly method of relationship measurement distance of method 1, and tool measurement 2, and estimates 16, and subject: geometry preliminary knowledge (1)--line and angle review content line, and segment, and Ray, and vertical, and parallel, and angle angle of classification (slightly) 17, and subject: geometry preliminary knowledge (2)--plane graphi, (1) determine standard vcs review content triangle, and edges shaped, and round, and fan axisymmetric graphics perimeter and area combination graphics of area subject : Preliminary knowledge (3)-review of solid content category 1-d shapes are divided into: cylinder and cone 2, column is divided iof the amount of canto: cuboid, square 3, cone cone of the features of cuboids and cubes relationship between characteristics of circular cone is slightly solid surface area and volume 1, size 2, table ...和本章的考核内容是

（一）知道随机变量的期望的定义和计算公式，性质。

（1）离散型：（2）连续型：（3）（4）

期望的性质：（1）E C=C

（2）E（kX）=kEX （3）E（X±Y）=EX±EY

（4）X,Y独立时，E（XY）＝（EX）（EY）

（二）知道方差的概念和计算公式以及方差的性质

∴X是离散型随机变量时

X是连续型随机变量时（2）计算公式（3）性质 ①DC＝0 ② ③D（X±Y）=DX+DY±2E[(X-EX)(Y-EY)]=DX+DY±2Cov(X,Y) ∴X,Y独立X,Y不相关时D(X±Y)=DX+DY Cov(X,Y)=E[(X-EX)(Y-EY)]

计算公式Cov(X,Y)=E(XY)－(EX)(EY) 相关系数定理X，Y独立

X，Y不相关（

）

第五章大数定律及中心极限定理