概率论
2018-05-29 14:00:20 0 举报AI智能生成
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1.Overview and Descriptive Statistics
Populations, Samples, and Processes
population
a well-defined collection of objects
census
desired information is available for all objects in the population
a sample
a subset of the population
a variable
any characteristic whose value may change from one object to another in the population
univariate data
consists of observations on a single variable
bivariate data
consists of observations on two variables
multivariate data
consists of observations on more than variables
descriptive statistics
graphical
histograms
boxplots
scatter plots
numerical
means
standard deviations
correlation coefficients
inferential statistics
Techniques for generalizing from a sample to a population
The population as consisting of all possible data that might
be made under similar experimental conditions. Such a population
is referred to as a conceptual or hypothetical population. There are
a number of problem situations in which we fit questions into the
framework of inferential statistics by conceptualizing a population.
The population as consisting of all possible data that might
be made under similar experimental conditions. Such a population
is referred to as a conceptual or hypothetical population. There are
a number of problem situations in which we fit questions into the
framework of inferential statistics by conceptualizing a population.
The relationship between probability and inferential statistics
Collection of Data
Simple random sample
Stratified random sample
Visulization of Data
Stem and Leaf plot
dot plot
histogram
Measure of Location
样本均值
中位数
Measures of Variability
Range
difference between the largest and smallest sample values
Deviations from the mean
Sum of deviations
样本方差和样本平方差
Population variance
2.Probability
2.1 Sample space and event
An experiment
is any action or process that generates observations.
The sample spaces
is the set of all the possible outcomes of an experiment.
An event E
is a subset of S
A is said to occur if the resulting experimental outcome is contained in A.
An event is any collection (subset) of outcomes contained in the sample space. An event is simple if it consists of exactly one outcome and compound if it consists of more than one outcome
Certain event E
Impossible event
Venn diagrams
Operation laws
2.2 Axioms of Probability
A mapping P satisfying above axioms is called a probability function.
Properties
Proofs
2.3 Counting techniques
排列
组合
性质
2.4 Conditional Probability
全概率公式、贝叶斯公式
2.5 Independent Event
Two events A and B are independent if P(A|B)=P(A) and are dependent otherwise.
Proof
Independence of More Than Two Events
3.Discrete Random Variables and Probability Distributions
3.1 Random Variables
A discrete random variable is an rv whose possible values either constitute a
finite set or else can be listed in an infinite sequence in which there is a first
element, a second element, and so on (“countably” infinite).
finite set or else can be listed in an infinite sequence in which there is a first
element, a second element, and so on (“countably” infinite).
3.2 Probability Distributions for Discrete Random Variables
Properties of c.d.f F(x)
Proofs
3.3 Expected Values
Proof
Rules of Expected Value
Proof
A Shortcut Formula
Proof
Rules of Variance
Proof
3.4 The Binomial Probability Distribution
Any random variable whose only possible values are 0 and 1 is called a
Bernoulli random variable.
Bernoulli random variable.
x—发生次数；n—实验次数；p—发生概率
Proof
3.5 The Poisson Probability Distribution
u=np=实验次数*发生概率
Proof
Proof
3.6 Hypergeometric and Negative Binomial Distributions
Hypergeometric Distribution
x—取中数；n—抽取总数；M—所要的最大数；N—样本总数
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