Problems 6, 13, 16, 21, 23, 25, 27c from the Chapter 3 handout.

G&S section 1.1, problems 1-5, 10.

Model solutions: http://www.math.dartmouth.edu/~doyle/docs/60.2012/hw/m60hw1.pdf

G&S section 1.1: 14,15,16

G&S section 1.2: 12,13,16,17,18,19,28

G&S section 2.1: 5,6,7,9

Model solutions: http://www.math.dartmouth.edu/~doyle/docs/60.2012/hw/m60hw2.pdf

G&S section 2.2: 5,6,12,20

G&S section 3.1: 22,23,24

G&S section 3.2: 6,10,13,18,34

For Ex. 34, Change `a good estimate ...' to `a bad estimate'--as Jie Zhong has pointed out. This incorrect estimate is based on a misprint in Feller. The correct estimate is
*m* = *n* log *n* + *n* log(1/log 2). Using your program, show that this is a good estimate.'

G&S section 4.1: 11,15,20,27,44-45 (with simulations), 55-60.

G&S section 4.2: 11,13.

G&S section 5.1: 6,16,21,28,42,45.

G&S section 5.2: 10,26,36,37

G&S section 6.1: 12,16a,19,20

G&S section 6.2: 3,15,17,18,23,24,25,26,27,29

G&S section 6.3: 7,12,13,17,18

Additional problems: Write Matlab code to simulate a Markov chain,
given by an arbitrary transition matrix *P*. Using this code

- Estimate the expected number of sunny days in the course of a 7-day week in the Land of Oz (cf. G&S, Example 11.1), if the week begins with a rainy day.
- For simple random walk on the integers {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, find by simulation the expected number of steps until you reach one of the two boundary points 0 and 10, starting from 3.

NOTE: Printed copies of G&S have screwed-up numbering for the later problems in section 6.2. To fix things up, relabel problem 26 as 25(b), 27 as 26, 28 as 27, 29 as 28 and 30 as 29. The result should agree with the online version here:

http://math.dartmouth.edu/~prob/prob/prob.pdf

G&S section 7.1: 4,8
(Use the Matlab function `conv` to do convolutions.)

G&S section 7.2: 5,15

For all of the following problems, compute the exact answer in addition to using the CLT approximation. For the CLT computations, whenever appropriate use the so-called 1/2-correction, as in G&S Example 9.2. Note that the answer key does not reliably use (or omit) the 1/2-correction.

G&S section 9.1: 1,3,5,7

G&S section 9.2: 1,4

- binomial
- Poisson
- geometric
- exponential
- Gaussian

Peter G. Doyle 2012-05-23