• Announcements: Please remember that the last homework assignment, HW12, is due by the end of Wednesday via Blackboard; solutions will be posted shortly. Also, you should have received an automated email from Lehman College with a link to provide instructor and course feedback through the SETL form. PLEASE SUBMIT YOUR ANSWERS, it is completely anonymous and of great importance for me and for the college. I will personally read all your comments, and use them to determine what is working well, and what should be done differently. Make your voices heard, for this and all your other courses! Thank you!

• Video 1: Introduction to Markov Chains: Download file or watch below

• Video 2: Example of a Markov Chain on the computer: Download file or watch below

• Video 3: Example of Markov Chain and transition probabilities after 2 and 200 steps: Download file or watch below

• Video 4: Chapman--Kolmogorov equations: Download file or watch below

• Video 5: Limiting behavior of (ergodic) Markov Chains as number of steps goes to infinity: Download file or watch below