頑想學概率：機率二 (Probability (2)) from Coursera

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Syllabus

Week 5

歡迎各位小夥伴加入「頑想學概率：機率二」！本課程延續「頑想學概率：機率一」，是前者的進階課程。在這一週我們將介紹專於於連續隨機變數的一個函數──機率密度函數 PDF ──並介紹連續機率分布。

WEEK 6

本週我們將延續上週還沒說完的連續機率分布，並介紹離散的隨機變數期望值。

WEEK 7

上週提到離散的隨機變數期望值，本週我們會談到離散的隨機變數期望值該怎麼算出來？在 7-2 和 7-3 我們會了解隨機變速的函數、條件的幾率分佈、和失憶性──之前我們有提到 Geometric Distribution 跟Exponential 都是失憶性的這種幾率分佈，那什麼叫失憶性 (Memoryless) 呢？

WEEK 8

前面幾個禮拜我們所考慮的問題都是只有一個隨機變數的狀況，這週我們要介紹聯合機率分布 (Joint probability distribution)、邊際機率分布 (Marginal probability distribution)，探討：如果有兩個隨機變數的話會有什麼不一樣的地方？期望值又是怎麼定義的？

WEEK 9

頑想學概率最後一週課程，內容一樣有趣又充實！如果有好幾個隨機變數我們把它加在一起，那加在一起之後產生的這個新的隨機變數，它的這個機率分布到底是什麼呢？MGF (Moment Generating Function) 是什麼？該怎麼用它找到隨機變數的機率分布？還有一定要知道的機率學中最重要的「萬佛朝宗」定理──中央極限定理！

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Explores the concepts of probability, which are standard in many industries

Taught by 葉丙成, who are recognized for their work in probability theory

Emphasizes developing an intuitive understanding of probability through gameplay

Introduces advanced concepts such as joint probability distribution and moment generating function

Assumes no prior knowledge of probability, making it suitable for beginners

Reviews summary

極佳的入門機率課程

這門課對於初學者來說是一個極好的機率入門課程，課程趣味橫生，寓教於樂。

課程內容深入淺出

"The best course for beginners"

教學品質良好

"great teacher"

學習過程生動有趣

"Great learning stuff, I enjoyed very much."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in 頑想學概率：機率二 (Probability (2)) with these activities:

制作概率模型幻灯片

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通过制作幻灯片，锻炼概率模型的建模和展示能力。

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选择一个概率模型
收集数据
拟合模型
制作幻灯片

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Career center

Learners who complete 頑想學概率：機率二 (Probability (2)) will develop knowledge and skills that may be useful to these careers:

Data Scientist

Data Scientists leverage their backgrounds in probability, statistics, computer programming, and business to build models and to solve complex problems. In order to succeed in this field, it's important to have a solid foundation in the fundamental theories of probability so that you can recognize situations in which probability can be applied appropriately. This course will introduce the fundamental concepts of probability, starting with the basics and progressing to advanced ideas. This knowledge can be used to establish a foundation for your Data Science career.

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Quantitative Analyst

Quantitative Analysts use their strong math, programming, and statistics skills to build and to evaluate complex financial models that aid in investment and trading decisions. It is important to have a background in probability and statistics in order to understand the risks associated with different investment strategies. This course will teach you a variety of probabilistic concepts which will help you as you develop your career as a Quantitative Analyst.

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Insurance Analyst

Insurance Analysts help insurance companies assess risk and to price insurance policies appropriately. Success in this role requires an understanding of probability in order to assess the risks associated with different insurance policies and to price those policies accordingly. This course will introduce you to the basic concepts of risk and probability which will directly support your work as an insurance analyst.

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Financial Consultant

Financial Consultants help their clients manage their money and plan for their future. It is important for financial consultants to have a solid understanding of probability and statistics so that they can assess risks and make recommendations about investments. This course will provide you with the foundational knowledge of probability that you need to succeed in your career as a financial consultant.

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Statistician

Statisticians collect, analyze, and interpret data. This data can be used to answer a variety of questions, ranging from the effectiveness of a new drug to the impact of a new policy. It's important for statisticians to have a strong understanding of probability and statistics, so that they can accurately interpret data and draw meaningful conclusions. This course will give you a foundation in the fundamental principles of probability, which will serve you well as you progress in your career.

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Business Analyst

Business Analysts identify, analyze, and solve business problems. It is important for business analysts to have a good understanding of probability and statistics so that they can analyze data and make recommendations about how to improve business outcomes. This course will provide you with the foundational knowledge of probability that you need to succeeding in your career as a Business Analyst

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Market Research Analyst

Market Research Analysts study market conditions and trends to help businesses make informed decisions about product development and marketing. It's important for market research analysts to have a solid understanding of probability and statistics, so that they can design research studies and analyze data accurately. This course will give you a deep dive into the fundamentals of probability, which will enhance your ability to make informed decisions in market research.

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Software Engineer

Software Engineers design, develop, and maintain software applications. Probability theory and related mathematical knowledge is less central to this field. However, an understanding of probability can inform effective decisions around testing, debugging, and developing software. This course can thus provide a strong foundation for you as you begin your career as a Software Engineer.

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Risk Manager

Risk Managers help organizations identify, assess, and mitigate risks. It's important for risk managers to have a strong understanding of probability and statistics so that they can understand the risks faced by their organizations and develop strategies to manage those risks. This course will provide you with the foundational knowledge of probability that you need to succeed in your career as a risk manager.

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Actuary

Actuaries use their mathematical and statistical skills to assess risk. They often work in the insurance industry, where they help to develop products and strategies to manage risk. An understanding of probability is essential for actuaries, as it allows them to accurately assess risks. This course will give you a strong foundation in the fundamentals of probability, which will serve you well as you progress in your career as an actuary.

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Economist

Economists study the production, distribution, and consumption of goods and services. They use their understanding of probability and statistics to analyze economic data and to make predictions about the future of the economy. This course will equip you with the foundational knowledge of probability that you need to succeed in your career as an economist.

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Data Analyst

Data Analysts clean, transform, and analyze data. They use their findings to make recommendations about how to improve business outcomes. It is important for data analysts to have a solid understanding of probability and statistics so that they can analyze data accurately and draw meaningful conclusions. This course will provide you with the foundational knowledge of probability that you need to becoming a Data Analyst.

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Operations Research Analyst

Operations Research Analysts use mathematical and analytical techniques to improve the efficiency of business operations. It is important for operations research analysts to have a strong understanding of probability and statistics so that they can develop effective optimization models. This course will provide you with the foundational knowledge of probability that you need to succeed in your career as an Operations Research Analyst.

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Machine Learning Engineer

Machine Learning Engineers design, develop, and maintain machine learning systems. It is important for machine learning engineers to have a solid understanding of probability and statistics so that they can develop effective machine learning algorithms. This course will provide you with the foundational knowledge of probability that you need to succeed in your career as a Machine Learning Engineer.

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Quantitative Trader

Quantitative Traders use mathematical and statistical models to trade financial instruments. It is important for quantitative traders to have a strong understanding of probability and statistics so that they can develop effective trading strategies. This course will provide you with the foundational knowledge of probability that you need to succeed in your career as a Quantitative Trader.

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