Probability Theory and Mathematical Statistics

3 Sep 2024 ~ 24 Dec 2024

Welcome to the homepage of Probability Theory and Mathematical Statistics !
Tips:
随机非随意，概率破玄机。
无序隐有序，统计解迷离。
《悟道诗》严加安

Course Introduction

Course number: 11100200 Credit: 3

The teaching content of this course is as follows:

Section	Content
1.1-5: Basic Concepts & Probability Axioms	Fundamental concepts of random events Probability axioms and properties Classical and geometric probability models
1.6-9: Conditional Probability & Independence	Conditional probability definition Total probability formula Bayes' theorem and applications Independence of events
2.3: Random Variables & Distributions	Definition of random variables Distribution functions (CDF) Discrete vs. continuous random variables Common probability distributions
2.4: Functions of Random Variables	Distribution transformations Methods for deriving distributions of functions Applications to probability calculations
3.1-3: Random Vectors	Joint distribution functions Discrete and continuous bivariate random variables Marginal distributions
3.4-5: Conditional Distributions & Transformations	Conditional distributions for random vectors Distributions of vector transformations Multivariate distribution techniques
4.2: Expectation & Variance	Mathematical expectation properties Variance and standard deviation Moments and moment-generating functions
4.3-4: Covariance & Characteristic Functions	Covariance and correlation coefficients Correlation functions Characteristic functions and properties
5.1-2: Limit Theorems	Law of Large Numbers (LLN) Central Limit Theorem (CLT) Applications and convergence concepts
6.1-2: Statistics	Sample statistics definitions Common statistical measures Data summarization techniques
6.3: Sampling Distributions	Distribution of sample statistics Chi-square, t, and F distributions Sampling distribution derivations
7.1-2: Point Estimation	Method of moments estimation Maximum likelihood estimation (MLE) Properties of point estimators
7.3-4: Estimation Properties & Intervals	Unbiasedness and efficiency Confidence interval construction Interval estimation methods
8.1-2: Hypothesis Testing Theory	Null and alternative hypotheses Type I/II errors and significance levels Test statistics and rejection regions
8.3: Normal Distribution Tests	Z-tests and t-tests Chi-square tests for variance ANOVA applications
8.4: Nonparametric Tests	Goodness-of-fit tests (e.g., Kolmogorov-Smirnov) Rank-based tests (e.g., Wilcoxon, Mann-Whitney) Distribution-free methods
Review	Comprehensive review of key concepts Problem-solving strategies Exam preparation

Course Resourse

Textbook of Probability Theory and Mathematical Statistics

Textbook.

Courseware of Probability Theory and Mathematical Statistics

Courseware(Part1).
Courseware(Part2).
Courseware(Part3).
Courseware(Part4).
Courseware(Part5).
Courseware(Part6).
Courseware(Part7).
Courseware(Part8).

Midterm of Probability Theory and Mathematical Statistics

Midterm.

Final of Probability Theory and Mathematical Statistics

Final.

Notes of Probability Theory and Mathematical Statistics

Notes(LaTeX Version) by Xipingo.

Tips of Probability Theory and Mathematical Statistics

Maybe you need not to 刷题 a lot this time. But it is important.

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