The purpose of this exercise is as follows.
Please familarize yourself with the following excerpt on plagiarism and collusion from the student handbook
By ticking the submission declaration box in Moodle you are agreeing to the following declaration:
Declaration: I am aware of the UCL Statistical Science Department’s regulations on plagiarism for assessed coursework. I have read the guidelines in the student handbook and understand what constitutes plagiarism. I hereby affirm that the work I am submitting for this in-course assessment is entirely my own.
Please do not write your name anywhere on the submission. Please include only your student number as the proxy identifier.
Let \(X\) be an aperiodic irreducible Markov chain on a finite state space \(S\). Let \(\pi\) be its stationary measure, and assume that \(X\) is started at \(\pi\). Let \(a, b \in S\).