概统

1. mutually exclusive

   \(A\cap{B}=\emptyset, i\neq{j}\)

2. collectively exhaustive

   \(A_1\cup{A_1}\cup\cdots\cup{A_i}=S\)

3. 贝叶斯公式、全概率、条件概率

4. 互斥且独立的条件：至少其中一个的发生概率为0
5. Random values: capital letters (X)

Consistant values: x

6. probability mass funcion

\(P_X(x)=P[X=x]\)

1. \(For\ any\ x, P_X（x）\geq0\)

2. \(\sum_{x\in{X}}{P_X(x)}=1\)

3. For any event \(B\subset{S(x)}\)
4. \(k-permutations\ of\ n: P(n, k)\)
5. \(Factorial:n!\)

6. Bernoulli Random Variable \(\(P_X(x)=\left\{\begin{matrix}1-p,\ x=0\\ \\ p,\ x=1\\ \\ 0,others \end{matrix}\right.\)\)

7. Geometric Random Variable

8. Binomial Random Variable
9. \(Var[X]=E[X^2]-E[X]^2\)

10. moment(矩)

    For random variable X: 1. The nth moment is \(E[X^n]\) 2. The nth central moment is \(E[(X-\mu _X)^n]\)

Classical Distribution

- Pascal: 第次k成立发生在第n次