1. Randomized trials

2. Sample space, random events

3. Frequency and probability

4. Other possible concepts

5. Conditional probability

6. Independence

1. Random variables

2. Discrete random variables and their distribution laws

3. Distribution function of random variables

4. Continuous random variables and their probability density

5. Functional distribution of random variables

1. Two-dimensional random variables

2. Marginal distribution

3. Conditional distribution

4. Mutually independent random variables

5. Function distribution of two random variables

1. Mathematical expectations

2. Variance

3. Covariance and correlation coefficient

4. Moments and covariance matrices

1.The law of large numbers

2. Central limit theorem

1. Random sample

2. Histograms and boxplots

3. Sampling distribution

1. Point estimate

2. Maximum likelihood estimation based on censored samples

3. Selection criteria for estimators

4. Interval estimation

5. Interval estimation of normal population mean and variance

6. Interval estimation of (0-1) distribution parameters

7. One-sided confidence interval

1. Hypothesis testing

2. Hypothesis test of normal population mean

3. Hypothesis test of normal population variance

4. The relationship between confidence intervals and hypothesis testing

5. Selection of sample size

6. Distribution fitting test

7. Rank sum test

8. p-value testing method for hypothesis testing problems

1. Analysis of variance in single factor test

2. Analysis of variance in two-factor test

3. Univariate linear regression

4. Multiple linear regression

1. Non-parametric bootstrap method

2. Parameter bootstrap method

1 Overview

2. Box plot

3. Hypothesis testing

4. Analysis of variance

5. Univariate linear regression

6.bootstrap methods, macros, VBA

1. The concept of random process

2. Statistical description of random processes

3. Poisson process and Wiener process

1. Markov process and probability distribution

2. Determination of multi-step transition probability

3. Traversability

1. The concept of stationary random process

2. Various ergodic properties

3. Properties of correlation functions

4. Power spectral density of stationary random processes