Homework Six: Due 22 October, 2010



Chapter 2.8:

  1. 2
  2. 6
  3. On a given day the stock market either goes up or down. Suppose the sequence of up and down days is given by UDDUD DUUDU UDDUD UUDDDD. Construct a Markov model for this sequence. According to your model, if the stock market went down today, what is the probability that it will go down tomorrow?
  4. Repeat the above analysis, but for the following sequence of up and down days: UUUDD DUUUD DDUUU DDDUUU. Do you think your Markov model is a good model of the process? Why or why not?

Chapter 2.7:

  1. 1
  2. 3

Proof by Contradiction:

  1. Prove that there are no integer solutions x,y to the equation x^2 - y^2 = 1.