Features
Features:

Product Tour >

Edraw AI >

Paid Plans:

Individuals >

Business >

Eduaction >
Resources
Blog

History

How-tos & Tips

Discovery

Biography

Business Analysis

Examples

AI concept Map

Free AI Mind Map Generator

Onenote Mind Map

Bcg Matrix Examples

Nike Marketing Strategy

Unilever SWOT Analysis

Make Mind Maps in Google Docs

Guide

FAQs

What's New

Resource Center
Templates
All Templates

Brain Storming Templates

Strategy and Planning Templates

Project Management Templates

Product Management Templates

Human Resources Templates

Agile Workflow Templates

Marketing Templates

Education Templates

Fun and Games Templates

User Gallery
Download
Pricing
Enterprise

MindMap Gallery Probability Theory and Mathematical Statistics

Probability Theory and Mathematical Statistics

The knowledge outline of probability theory and mathematical statistics covers both probability theory and mathematical statistics, including probability, frequency, samples, the law of large numbers, parameter estimation, etc. Learners can add content based on their own understanding based on this template to improve learning efficiency.

Edited at 2024-03-02 22:31:28

PlotWizard

Probability Theory and Mathematical Statistics

PlotWizard

Recommended to you
Outline

Fundamentals of Probability and Molar Mass
- 55
Ariane
Probability Theory and Mathematical Statistics
- 203
PlotWizard
Probability Theory and Mathematical Statistics
- 146
PlotWizard
Probability Theory Course Summary
- 47
PlotWizard
General Chapter 3 Two-Dimensional Random Variables Mind Map
- 96
PlotWizard
General Chapter 3 Two-Dimensional Random Variables Mind Map
- 49
PlotWizard
01_Events and Probability
- 45
PlotWizard

Probability Theory and Mathematical Statistics

1. Basic concepts of probability theory

1. Randomized trials

Can be repeated under the same conditions

Each experiment has more than one possible outcome, and all possible outcomes of the experiment can be clarified in advance

It is not possible to determine which outcome will occur until an experiment is conducted

2. Sample space, random events

Sample space

The set of all possible outcomes of a randomized trial

sample point

elements of sample space

Random events (events)

subset of sample space

basic events

a random event consisting of a sample point

special random events

inevitable event

impossible event

event relationship

Subset

The occurrence of A will inevitably lead to the occurrence of B

equal

and events

accumulated events

bad event

mutually exclusive events

Opposition events

Opposite event of A

3. Frequency and probability

4. Other possible concepts

5. Conditional probability

6. Independence

2. Random variables and their distribution

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

3. Multidimensional random variables and their distribution

1. Two-dimensional random variables

2. Marginal distribution

3. Conditional distribution

4. Mutually independent random variables

5. Function distribution of two random variables

4. Numerical Characteristics of Random Variables

1. Mathematical expectations

2. Variance

3. Covariance and correlation coefficient

4. Moments and covariance matrices

5. The law of large numbers and the central limit theorem

1.The law of large numbers

2. Central limit theorem

6. Sample and sampling distribution

1. Random sample

2. Histograms and boxplots

3. Sampling distribution

7. Parameter estimation

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

8. Hypothesis testing

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

9. Variance analysis and regression analysis

1. Analysis of variance in single factor test

2. Analysis of variance in two-factor test

3. Univariate linear regression

4. Multiple linear regression

10. Bootstrap method

1. Non-parametric bootstrap method

2. Parameter bootstrap method

11. Application of Excel software in mathematical statistics

1 Overview

2. Box plot

3. Hypothesis testing

4. Analysis of variance

5. Univariate linear regression

6.bootstrap methods, macros, VBA

12. Random process and its statistical description

1. The concept of random process

2. Statistical description of random processes

3. Poisson process and Wiener process

13. Markov chain

1. Markov process and probability distribution

2. Determination of multi-step transition probability

3. Traversability

14. Stationary random process

1. The concept of stationary random process

2. Various ergodic properties

3. Properties of correlation functions

4. Power spectral density of stationary random processes