Markov Chains & Matrices: Part 1 скачать в хорошем качестве

Markov Chains & Matrices: Part 1

Learn Markov Chains with a Sports Fan Example: In this detailed video lesson, we explain the concept of Markov Chains using a practical example involving sports team fans in a fictional town. Discover how the townspeople, divided into 70% Aardvark fans and 30% Bronco fans, experience an annual shift in allegiance. Specifically, each year, 10% of Aardvark fans switch to supporting the Broncos, while 15% of Bronco fans convert to Aardvark fans, leading to a dynamic change in fan distribution over time. We start by defining a state vector (S₀), representing the initial fan distribution: 0.7 for Aardvark supporters and 0.3 for Broncos. Using a Markov Chain framework, particularly a transition matrix, we demonstrate how to map these annual fan changes. The matrix contains probabilities defining how many fans stay loyal or switch their team allegiance, including 0.9 Aardvark loyalty and 0.1 switching rate, with equivalent probabilities for Bronco supporters. By multiplying the transition matrix with the state vector, you can forecast the changes in fan distribution in subsequent years. This video emphasizes the necessity of understanding the transition matrix and state vector to predict transitional changes in systems modeled by Markov Chains. Check out the video to enhance your grasp of Markov Chains and how they apply to real-world scenarios, such as predicting shifts in fan allegiance over time. --- *Key Topics Covered:* Explanation of Markov Chains Practical application using sports fans State vector and transition matrix concepts Calculating future probabilities and distributions *Don't Miss:* Step-by-step breakdown of calculations Visual demonstrations of yearly fan distribution changes If you find this content insightful, consider subscribing for more educational videos on mathematical modeling and probabilistic systems. Find 100's more videos linked to the Australia Senior Maths Curriculum at http://mathsvideosaustralia.com/