# Homework for Math 564

Homework will be assigned weekly, to be handed in about a week later in class.

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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