course | course_year | question_number | tags | title | year | |||
---|---|---|---|---|---|---|---|---|
Markov Chains |
IB |
22 |
|
Paper 1, Section II, H |
2020 |
Let $\left(X_{n}\right){n \geqslant 0}$ be a Markov chain with transition matrix $P$. What is a stopping time of $\left(X{n}\right)_{n \geqslant 0}$ ? What is the strong Markov property?
A porter is trying to apprehend a student who is walking along a long narrow path at night. Being unaware of the porter, the student's location
(a) By setting up an appropriate Markov chain, show that for
(b) Show that the expected time for the porter to catch the student, i.e. for their locations to coincide, is
[You may use without proof the fact that the time for the porter to catch the student is finite with probability 1 for any