Probability Theory and Mathematical Statistics (Overview of Knowledge Points)

The reference material comes from "Dr. Monkey's Love Lecture Series" at station B here

1. Part of Probability Theory

Random Events and Probability

1. Classical outline

2. Geometric outline

3. The probability of an event

4. Independence of events

5. Conditional probability

6. Full probability formula

7. Bayesian formula

2. Mathematical Statistics Section

| Continuous vs Discrete

discrete

1. One-dimensional discrete distribution law

**Note: **Another way of writing the distribution law

2. One-dimensional discrete type to find expectation, variance

Note: E ( X 2 ) E(X^2) is calculated above$E(X^2)$, the green icon is not strictly speaking$X^{The\; expectation\; of\; 2}$ , because$(-2{)}^2$ and$(2{)}^2$ is actually a situation and should be merged. However, the title only requires calculation results, so it will not have any effect.

3. Two-dimensional discrete distribution law

4. Two-dimensional discrete type to find the edge distribution law

continuous

One-dimensional continuous random variable

Topic one:

Notice:

for the probability density from $-\infty -+\infty$ integrates to 1

The unknown is only $M$时，$f_M\left(m\right)$ can be abbreviated as$f(m)$

One-dimensional continuous type to find F

Expressed as the corresponding probability and then solved

One-dimensional continuous type known F to find f

$f_A(a)=F_A^{{}^{\prime }}\left(a\right)$

One-dimensional continuous type to find F

Common method: All questions can be used


Formula method:
Condition: If $f_X(x)\ne$In the interval of$0$$Y=g\left(X\right)$ is monotonically increasing or monotonically decreasing

Step 1 & Step 2

Step 3:

Step 4:

One-dimensional continuous type to find the expectation, variance

Request $E(X)$

Request $E(X^2)$

Find $D(X)$