MindMap Gallery Probability Theory and Mathematical Statistics
A particularly comprehensive mind map that summarizes the basic concepts of probability theory, random variables and their distribution, random vectors, numerical characteristics, mathematical statistics, Point estimate etc.
Edited at 2024-01-13 22:48:46This is a panoramic infographic—currently sweeping across the web—illustrating the comprehensive applications of OpenClaw, a popular open-source AI agent platform. It systematically introduces this intelligent agent framework—affectionately dubbed "Lobster Farming"—helping readers quickly grasp its core value, technical features, application scenarios, and security protocols. It serves as an excellent introductory guide and practical manual.
這是一張最近風靡全網關於熱門開源AI代理平台OpenClaw的全網應用全景圖解。它系統性地介紹了這款被稱為「養龍蝦」的智慧體框架,幫助讀者快速理解其核心價值、技術特性、應用場景及安全規範,是一份極佳的入門指南與實操手冊。此圖主要針對希望利用AI建構自動化工作流程的技術從業人員、中小企業主及效率追求者,透過9大模組層層遞進,全面剖析了OpenClaw從概念到落地的整個過程。 圖中核心內容首先釐清了「養龍蝦」指涉的是OpenClawd開源智能體,並強調其本質是「AI基建」而非一般聊天機器人。隨後詳細比較其與傳統AI助理的區別,擁有記憶管理、權限控制、會話隔離和異常恢復四大基礎能力,支援跨平台存取和多模型相容(如GPT、Claude、Ollama)。同時,圖解提供了完整的部署方案(雲端/本地/Docker),並列舉了辦公室自動化、內容創作、資料收集等五大應用程式場景。此外,還展示了其火爆程度、政府與大廠佈局、安全部署建議及適合/不適合的人群分類。幫助你快速掌握OpenClaw技術架構與應用價值,指導個人或企業建構AI自動化系統,規避資料外洩與權限失控風險,是學習「執行式AI」轉型的權威參考圖譜。
本圖由萬興腦圖繪製,是針對IT研發崗位的結構化個人履歷模板,完整涵蓋求職核心資訊模組。基本資訊區包含姓名、電話、信箱、求職意願及GitHub連結;專業概要要求以2-3句提煉核心優勢;工作經驗以「公司A高級Java開發工程師」為例,以「透過(行動),達成(量化成果)」格式呈現微服務架構設計、系統效能優化、團隊技術規範制定等職責,公司B經歷則聚焦功能模組開發與Elasticsearch搜尋優化;技能專長分程式語言、後端框架、中介軟體、資料庫、容器雲等維度,清楚展示技術堆疊;專案成果以「電商平台秒殺系統」為例,說明技術棧、架構設計、個人貢獻(Redis Lua庫存原子扣減)及KPI;教育背景包含一流大學電腦專業學歷,以及AWS認證解決方案架構師、軟考中級軟體設計師證書。模板邏輯嚴謹,涵蓋IT研發求職全流程關鍵訊息,幫助求職者清晰、量化展示專業能力。
This is a panoramic infographic—currently sweeping across the web—illustrating the comprehensive applications of OpenClaw, a popular open-source AI agent platform. It systematically introduces this intelligent agent framework—affectionately dubbed "Lobster Farming"—helping readers quickly grasp its core value, technical features, application scenarios, and security protocols. It serves as an excellent introductory guide and practical manual.
這是一張最近風靡全網關於熱門開源AI代理平台OpenClaw的全網應用全景圖解。它系統性地介紹了這款被稱為「養龍蝦」的智慧體框架,幫助讀者快速理解其核心價值、技術特性、應用場景及安全規範,是一份極佳的入門指南與實操手冊。此圖主要針對希望利用AI建構自動化工作流程的技術從業人員、中小企業主及效率追求者,透過9大模組層層遞進,全面剖析了OpenClaw從概念到落地的整個過程。 圖中核心內容首先釐清了「養龍蝦」指涉的是OpenClawd開源智能體,並強調其本質是「AI基建」而非一般聊天機器人。隨後詳細比較其與傳統AI助理的區別,擁有記憶管理、權限控制、會話隔離和異常恢復四大基礎能力,支援跨平台存取和多模型相容(如GPT、Claude、Ollama)。同時,圖解提供了完整的部署方案(雲端/本地/Docker),並列舉了辦公室自動化、內容創作、資料收集等五大應用程式場景。此外,還展示了其火爆程度、政府與大廠佈局、安全部署建議及適合/不適合的人群分類。幫助你快速掌握OpenClaw技術架構與應用價值,指導個人或企業建構AI自動化系統,規避資料外洩與權限失控風險,是學習「執行式AI」轉型的權威參考圖譜。
本圖由萬興腦圖繪製,是針對IT研發崗位的結構化個人履歷模板,完整涵蓋求職核心資訊模組。基本資訊區包含姓名、電話、信箱、求職意願及GitHub連結;專業概要要求以2-3句提煉核心優勢;工作經驗以「公司A高級Java開發工程師」為例,以「透過(行動),達成(量化成果)」格式呈現微服務架構設計、系統效能優化、團隊技術規範制定等職責,公司B經歷則聚焦功能模組開發與Elasticsearch搜尋優化;技能專長分程式語言、後端框架、中介軟體、資料庫、容器雲等維度,清楚展示技術堆疊;專案成果以「電商平台秒殺系統」為例,說明技術棧、架構設計、個人貢獻(Redis Lua庫存原子扣減)及KPI;教育背景包含一流大學電腦專業學歷,以及AWS認證解決方案架構師、軟考中級軟體設計師證書。模板邏輯嚴謹,涵蓋IT研發求職全流程關鍵訊息,幫助求職者清晰、量化展示專業能力。
Probability Theory and Mathematical Statistics
Basic concepts of probability theory
Four formulas
addition
AUB, AB at least one occurs
Subtraction
division
multiplication
P(AB)=P(A/B)*P(B)
independent
Classical concept
Total probability, Bayesian formula
Pairwise mutually exclusive: two sets have no intersection
total probability formula
Bayes' formula: the probability of the first small event occurring when a complex event occurs
Bernoulli profile
Random variables and their distribution
discrete random distribution
tabular method
Be clear and concise in the form of a list
General method
binomial distribution
Maximum number of successes
Distribution of continuous random variables
X~U(a,b) is uniformly distributed X~E(m) is an exponential distribution X~N(u,6) is a normal distribution X~b(1,p) is a two-point distribution X~b(n,p) is a binomial distribution
Evenly distributed
normal distribution
Chart method
Exploiting the symmetry of normal distribution images
Standardization method
Convert normal distribution into standard normal distribution
Distribution of discrete random variable X
Distribution of continuous random variable X
random vector
two-dimensional random variable
Discrete
Find the distribution
Find the marginal distribution
Find conditional distribution
Find whether to independently verify whether the union is equal to the product of the edges
continuity
Normative
The probability that the joint distribution is on a certain interval
edge density function
The marginal density function of y can be roughly regarded as the integral of x when y is fixed.
Conditional Probability
subtopic
Distribution of two-dimensional random vectors
Discrete random variable
continuous random variable
digital features
Expectation and variance
Variance = Expectation of Squares Expectation of Squares
Chebyshev's inequality
discrete covariance
continuity covariance
mathematical statistics
various distributions
central limit theorem
point estimate
distance estimation method
maximum likelihood estimation
The samples are independent and identically distributed
Both the normal distribution and the chi-square distribution are additive
Irrelevance cannot lead to independence. Independence must not be relevant.
The words "at least" and "at most" appear to take advantage of opposing events.
Included here are geometric sketches 1. Analyze the number of variables it includes 2. List and solve geometric relationships
1. Divide the problem into two stages. For example: stage one is picking people, stage two is the probability of color blindness. 2. Let the events be A, B, C, etc. 3. Use total probability or Bayesian formula to solve
Whatever you ask for, get it