頑想學概率：機率二 (Probability (2))

National Taiwan University via Coursera

Go to Course: https://www.coursera.org/learn/prob2

Introduction

# Course Review: Probability (2) on Coursera ## Overview "Probability (2)" – or "頑想學概率：機率二" – is an engaging and comprehensive introduction to probability, continuing the foundations laid in its predecessor, "Probability (1)." This course, presented in Mandarin, emphasizes key concepts while incorporating a unique twist: assignments are designed around a competitive online gaming environment developed by the Computer Science Department at National Taiwan University. This innovative approach ensures that learners not only grasp theoretical concepts but also apply them in creative ways, enhancing their skills in probability. ## Course Structure ### Week 5: Introduction to Probability Density Functions (PDF) The course kicks off with the essential concept of continuous random variables, introducing the Probability Density Function. This week sets the stage for understanding continuous probability distributions, emphasizing intuitive insights into how these functions behave. ### Week 6: Delving Deeper into Continuous Probability Distributions Building on the previous week's content, this week further explores continuous probability distributions while also introducing the expected value of discrete random variables. The emphasis on application and practical interpretation makes it easier for students to connect concepts with real-world scenarios. ### Week 7: Understanding Expectation and Memoryless Properties This week focuses on calculating the expected values of discrete random variables. A particularly intriguing part of the lesson is the exploration of memoryless distributions, such as the Geometric and Exponential distributions. This concept adds depth to students' understanding of random variables and their properties. ### Week 8: Joint and Marginal Probability Distributions Week 8 shifts the focus to joint and marginal probability distributions. Introduced are scenarios with multiple random variables, prompting students to consider how these variables interact and how their combined probabilities differ from those of single random variables. The complex relationships are simplified through clear examples and applications. ### Week 9: Moment Generating Functions and the Central Limit Theorem In the final week, the course culminates in understanding the concept of Moment Generating Functions (MGF) and the integral Central Limit Theorem, famously referred to as the “万佛朝宗”定理. With this, students are equipped with tools to analyze the probability distributions of sums of random variables, a common scenario in practical applications of statistics. ## Review The course excels in providing a well-structured approach to complex topics in probability, making them accessible and engaging. The use of an online gaming framework for assignments adds a layer of interaction that many students will find enjoyable, fostering a deeper connection with the material. The instruction is clear and progresses logically, with ample opportunity for practice through interactive elements. Furthermore, the integration of both discrete and continuous probability concepts prepares students for real-world applications of probability in fields such as data science, finance, and engineering. ## Recommendation If you are someone interested in enhancing your understanding of probability or looking to apply statistical concepts in practical ways, "Probability (2)" on Coursera comes highly recommended. The engaging format, coupled with a strong educational foundation, makes it an excellent choice, whether you are a student, professional, or simply a curious learner. However, prior completion of “Probability (1)” or a basic understanding of the foundational principles of probability will enhance your experience and understanding throughout this course. Dive into this course to not only learn but also play your way to a better grasp of probability!

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！