| Section of the book | Exercise pages | Exercises | Due date |
|---|---|---|---|
| 1.1 | 8-9 | 1.1.1, 1.1.2, 1.1.3, 1.1.6 | Wednesday, Sep. 9 |
| Let Xn be a two-state Markov chain
with transition probabilities p1,2=a and p2,1=b. Show that Yn=(Xn+1,Xn) is also a Markov chain. Find its transition matrix. |
Wednesday, Sep. 9 | ||
| 1.2 | 12 | 1.2.2 | Wednesday, Sep. 9 |
| 1.3 | 18-19 | 1.3.2, 1.3.3 | Friday, Sep. 18 |
| Consider a Markov chain Xn with states {0,1,...,N}. Let q=1-p. Let pi,i+1=p for i=0,1,...,N-1 and pi,i-1=q for i=1,..,N-1. Assume pNN=1. Compute Pi(H{0} is finite). |
Friday, Sep. 18 | ||
| 1.4-1.6 | 1.4.1, 1.6.1 | Friday, Oct. 2 | |
| Prove that 2D random walk is recurrent by counting paths. Look at the proof for 3D random walk and modify it. | Friday, Oct. 2 | ||
| 1.7-1.8 | 1.7.3, 1.7.5, 1.8.3 | Wednesday, Oct. 14 | |
| 1.9-1.10 | 1.9.2, 1.10.2 | Monday, Oct. 26 | |
| 2.3-2.4 | 2.3.2, 2.4.4, 2.4.5 | Wednesday, Nov. 11 | |
| 2.8-3.6 | 2.8.2, 3.4.1, 3.6.3 | Monday, Nov. 30 | |
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