Probability Basics:
## 随机变量的概率分布，随机变量的函数的概率分布，条件概率，联合概率
## 期望，方差，协方差，相关系数
## 里面有各种分布：
### 典型离散分布：
0-1分布：取值不是0就是1，两个概率都是50%, 只实验一次
伯努利分布： 也是只有两种结果，但是概率不一定是50%，所以0-1分布是伯努利分布的一种特例，只实验一次(也叫伯努利实验)
二项分布： 伯努利实验 做n次，有k成功的概率， 是一个二项式， n次实验之间是独立的
泊松分布： 一段时间内某个事件出现k次的概率，比如一天内发生火灾的次数，交通事故的次数，
泊松分布可作为二项分布的极限而得到。也就是n取无限大的时候
### 典型的连续分布：
正态
## 分布函数F和概率密度f：
对于连续随机变量 F(x)是指 随机变量X取值<=x的概率
f(x) 表示X取x的概率密度，一般需要通过积分求得分布函数， 要求概率密度，也是通过分布函数进行求导(微分)得到Parameter Estimation:
Estimate the parameters of the overall distribution function based on the sampled samples: Note that the estimated target object is the parameter in the distribution
## Point estimation:
maximum likelihood estimation: Find a parameter, based on the existing samples, that maximizes the probability of generating these samples from this distribution jointly ---Transform into the problem of finding extreme values: two methods: 1. Find the solution of the partial derivative equation system (it must be derivable), 2. Gradient descent (does not require derivation, but it may fall into a local optimum, from In terms of performance, it is best to use stochastic gradient descent)
moment estimation: I still don’t understand
it
.
hypothetical test:
According to the sampling sample, to verify the hypothesis that the overall distribution belongs to a certain distribution, or the overall distribution is known, assuming that a certain parameter is a certain value, it is necessary to make a final decision based on the sample, whether to accept this hypothesis, or consider this hypothesis Is it reasonable?
There are various testing methods.
The specific theory is not very clear
, but we can check it with reference to various examples, and we can look up the table.
Theorem of Large Numbers, Central Limit Theorem:
When multiple independent variables act together, they generally obey the normal distribution (also called Gaussian distribution).
When the number of samples increases, the expectation is approximately equal to the mean