Problems are from, *An Introduction to
Stochastic Modeling* by S. Karlin and H. Taylor, or
in a PDF file found by following the links. (The convention here is that
II.1: E1 refers to Exercise 1 of section 1 of Chapter II. While II.3: P4 refers
to Problem 4 of section 3 of Chapter II.)

**Homework 1 (due Monday, April 7)**

Please click
here for the first assignment.

**Homework 2 (due Monday, April 14)**

IV.1 (p. 208 --): E5, E8, P1, P5

IV.3 (p. 243 --): E1, E2, E3,

IV.4 (p.254 -- ): E2

**Homework 3 (due Monday, April 21)**:

Please see the beginning of the Lecture notes:
180Notes20080414 for the
third homework assignment.

**Homework 4 (due Monday, April 28)**:

VI.1 (p. 342 --): E1, E2, E5, P3, P5*, P8**

IV.2 (p. 353 --): E1, P2***

* Please show that *W*_{1} and W_{2}
- *W*_{1 }are independent exponentially distributed random
variables by computing P(*W*_{1} > t and W_{2} - *W*_{1
}> s) for all s,t>0.

**Hint: you can save some work using what we already have
seen about two state Markov chains, see the notes or sections VI.3 or VI.6 of
the book.

*** Depending on how you choose to do this problem you may find Lemma 2.7 in the
lecture notes useful.

**Homework 5 (due Monday, May 5)**:

**VI.2 (p. 353 --): **P2.3*

VI.3 (p. 365 --): E3.1, E3.3, P3.3, P3.4

VI.4 (p. 377 --): E4.2, P4.1

*Hint: look at the picture on page 345 to find an
expression for the area in terms of the *S*_{k}.

**____________________________________________**

**Test #1 is on Friday May 9**

**________________________________________________________**

**Homework 6 (due Monday, May 12)**:

**VI.4 (p. 377 --):** P4.3

**VI.5 (p. 392 --):** P5.2

**VI.6 (p. 405-):** P6.2

**Homework 7 (due Monday, May 19)**:

**VII.1 (p. 424-426):** Ex. 1.2, 1.3; Pr. 1.1, 1.3

**VII.2 (p. 431-432):** Ex. 2.1

**VII.3 (p. 435-437):** Ex. 3.1*, 3.3**; Pr. 3.2

*Write the event {N(t)=n and W_{N(t)+1}>t+s} purely in terms of the Poisson
process, N. Then use your knowledge of N in order to do the computations.

**Use facts you know about Poisson processes and make use of Ex. 3.1.

**No Homework (due Monday, May 26 Holiday)**:

**Homework 8 (due Monday, June 2)**:

**VII.3 (p. 435-437):** Pr. 3.4

**VII.4 (p. 445-447):** Ex. 4.2, 4.3, 4.5; Pr. 4.1, 4.5

**VII.5 (p. 455-457):** Ex. 5.1; Pr. 5.1, 5.4

~~
~~**VIII.1 (p. 487-491):** Ex. 1.1, 1.4, 1.5; Pr. 1.1
(I am going to change these!)

**________________________________________________________**

**The Final exam is on Wednesday, June
11 at 8:00 -- 11:00 AM ****
in
YORK 4080A. **

**
Please bring a blue book or paper!**

You may bring one 8 1/2 X 11 sheet (front and back) of notes if you wish.