Enroll Course: https://www.coursera.org/learn/prob2
Are you ready to take your understanding of probability to the next level? If you’ve already grasped the fundamentals from “Probability (1)”, then Coursera’s “Probability (2)” course, also known as “頑想學概率：機率二”, is your next exciting step. This course, developed in collaboration with National Taiwan University’s Electrical Engineering department, offers a refreshing approach to learning probability by integrating it with a fun, competitive online game.
This isn’t just another dry lecture series. The core philosophy here is learning through play. The assignments are designed as engaging games, making the process of grasping complex probability concepts enjoyable and intuitive. You’ll find yourself quickly developing a keen insight into probability and its real-world applications, all while having a blast.
Let’s dive into what you can expect in the later weeks of the course:
**Week 5: Diving into Continuous Random Variables**
This week marks a significant step into the realm of continuous random variables. You’ll be introduced to the Probability Density Function (PDF), a crucial tool for understanding continuous probability distributions. Get ready to explore how these distributions work and their properties.
**Week 6: Continuing Continuous Distributions & Discrete Expectations**
Building on Week 5, we’ll continue our exploration of continuous probability distributions. The focus then shifts to the concept of expected value for discrete random variables. Understanding expectation is key to quantifying the average outcome of a random process.
**Week 7: Calculating Discrete Expectations & Memorylessness**
This week delves deeper into calculating the expected value of discrete random variables. You’ll also learn about functions of random variables and conditional probability distributions. A particularly interesting concept introduced is ‘memorylessness’, a property shared by distributions like the Geometric and Exponential distributions. What does it mean for a random process to forget its past?
**Week 8: Joint, Marginal, and Expected Values of Multiple Variables**
So far, we’ve primarily dealt with single random variables. This week, the course expands your horizons to consider scenarios with multiple random variables. You’ll be introduced to Joint Probability Distributions and Marginal Probability Distributions, and understand how the concept of expected value is extended to these multi-variable situations.
**Week 9: Sums of Random Variables, MGFs, and the Central Limit Theorem**
In the final week, you’ll tackle even more advanced topics. What happens when you sum several random variables? This week explores the probability distribution of the resulting sum. You’ll also learn about Moment Generating Functions (MGFs) and how they can be used to determine probability distributions. The grand finale is the Central Limit Theorem, a cornerstone of probability theory, often referred to as the ‘king of all theorems’.
**Recommendation:**
If you’re looking for a probability course that is both rigorous and engaging, “Probability (2)” is an excellent choice. The gamified approach makes learning enjoyable, and the syllabus covers essential advanced topics that are crucial for anyone serious about statistics, data science, or engineering. Highly recommended for intermediate learners looking to solidify their probabilistic foundation!
Enroll Course: https://www.coursera.org/learn/prob2