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頑想學概率：機率二 (Probability (2))

葉丙成

這是一個機率的入門課程，著重的是教授機率基本概念。另外我們的作業將搭配臺大電機系所開發的多人競技線上遊戲方式，讓同學在遊戲中快樂的學習，快速培養同學們對於機率的洞察力與應用能力。

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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。

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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

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Reviews summary

頑想學概率：機率二 (probability (2))

根據學習者反饋，本課程作為「頑想學概率：機率一」的進階，提供了扎實的機率理論基礎內容深度足夠，特別是在連續隨機變數、聯合分佈、MGF、中央極限定理等進階概念的講解。許多學生認為課程的講解非常清楚易懂，邏輯結構清晰，有助於建立完整的機率觀念。搭配臺大電機系開發的線上遊戲，讓學習過程生動有趣，能將理論應用於實踐。雖然對部分初學者來說可能稍有難度，需要先修知識，但整體而言是學習機率的極佳選擇。

學習後對機率有更全面系統的理解。

"這門課幫助我串聯起機率一和機率二的知識，建立了一個更完整的機率框架。"

"透過這門課，我對機率有了更系統性的理解，不再是零散的概念。"

"課程結構安排得很好，讓我能一步步建立完整的機率觀念，對於後續學習非常有幫助。"

"學完這兩門課（機率一、二），我覺得自己對機率的掌握更全面了。"

結合線上遊戲，增加學習趣味與應用。

"搭配遊戲學習的方式非常有趣，讓我可以在實戰中應用學到的機率知識，遊戲設計得很巧妙！"

"我很喜歡課程搭配的遊戲，讓抽象的機率概念變得具體，玩遊戲的同時也加深了理解。"

"遊戲設計雖然簡單，但和課程內容連結緊密，讓學習不只是聽課，多了很多互動和應用的機會。"

"課程結合遊戲是個創新的嘗試，讓原本可能枯燥的機率學習變得生動許多。"

老師的教學方式有助於理解複雜概念。

"老師講得很清楚，原本覺得機率很難，但聽了老師的講解後，突然就融會貫通了！非常推薦！"

"老師講解非常有條理且清晰，非常適合當作入門，甚至有修過機率論的人來複習也很不錯，有助於建立完整的機率觀念。"

"老師對於機率的講解非常清楚，即使是很抽象的概念，也能用例子輔助說明，讓我學得很有動力。"

"講師的講解非常到位，讓原本複雜的機率問題變得簡單，讓我對機率有了全新的認識。"

涵蓋進階機率概念，深度足夠。

"課程內容由淺入深、脈絡清晰，老師用簡單易懂的方式教導機率。尤其課程有包含中央極限定理，是很完整的機率課程。"

"這門課對於機率的概念幫助非常大，是學習連續機率密度、期望值、聯合機率、MGF、中央極限定理等知識的好課程！"

"內容非常紮實，讓我可以把很多之前覺得模模糊糊的機率概念弄得更清晰，尤其最後的中央極限定理，老師把觀念講得很透徹。"

"課程內容很棒，把機率二的部分教得很仔細，搭配機率一讓機率的基礎更穩固，也理解中央極限定理背後的意義。"

建議先修機率一，確保學習順暢。

"建議修習此課程前，先完成「頑想學概率：機率一」，否則某些觀念可能會跟不上。"

"如果沒有機率一的基礎，直接學機率二可能會有點吃力，內容難度有提升。"

"這門課確實是機率二的進階，需要有機率一的基礎才能更好地理解後面的內容。"

"課程中有些地方假設學生已具備機率一的知識，若無則需要額外補充學習。"

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
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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.

See salaries and explore the career path for Data Scientist

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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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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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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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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Reading list

We've selected 12 books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in 頑想學概率：機率二 (Probability (2)).