Homework

Assignment 1 due September 11 from Chapter 1 Markov Chains:

9.1 (explain your answer), 9.2, 9.5, 9.7 (a)

Assignment 2 due September 25 from Chapter 1 Markov Chains:

9.25, 9.12 (a), (b), (c) [Hint: Stationary distributions for $p^{2}$ form a one parameter family]

Assignment 3 due October 9 from Chapter 2 Martingales:

5.2 (a) [8pt], 5.3 [8pt], 5.5 (a), (b), (c) [16pts for all three]

Assignment 4 due October 23

Ch 2: 5.12, 5.13 Ch 3: 7.5, 7.22 (a), (b), (d) (in (d) it is assumed that it takes no time to answer a call and the calls arriving during the breaks are lost, they are not waiting to get answered)

Assignment 5 due November 6, Chapter 4:

8.1 (9 pts. In (a) the question is to find and explain how you find the matrix $Q$. In (b) by ``how long doest it take'' is meant the expected time),

8.4 (7 pts for (a), 2 pts for (b)),

8.7

8.15 (7 pts for (a), 2 pts for (b))

Assignment 6 due November 25:

Chapter 4: 8.25, 8.35 (you are asked to find the so-called Erlang's distribution)

Chapter 5: 5.1 (Explain your answer), 5.24 [(a) 6 pts, (b) 3 pts]

Assignment 7 due December 11

Chapter 5: 5.31

Chapter 6: 6.5 (Only do it for $t=1,x=0$. At a certain point you will have to explain that the integral of a Gaussian process is Gaussian, 3 pts for that.), 6.8, 6.21

Final: December 16, 4:40=6:40. The final is composed of four even number problems. There is one problem on Markov chains-Martingales, one on the Poisson process, one on the renewal processes, and the last one on Brownian motion.