# Math 60, Spring 2012, important dates

## HW1 DUE Tuesday 3 April

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

## HW2 DUE Tuesday 10 April

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

## HW3 DUE Tuesday 17 April

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.'

## TEST 1, Tuesday 17 April

Combinatorial probability, as in G&S Chapters 1 and 3 (except 3.3), and Chung.

## HW4 DUE Tuesday 1 May

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

G&S section 4.2: 11,13.

## HW5 DUE Tuesday 8 May

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

## PROJECT 1 DUE Thursday 10 May

Project 1 due in printed and electronic form.

## HW6 DUE Thursday 17 May

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

1. 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.
2. 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:

## HW7 DUE Thursday 24 May

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

## VERY SHORT QUIZ on important distributions and Stirling's formula

I'll ask you to give formulas for the densities of the following distributions, and to identify their mean, variance, and standard deviation:
• binomial
• Poisson
• geometric
• exponential
• Gaussian
I'll also ask you for Stirling's formula.

## PROJECT 2 DUE Thursday 31 May

Project 2 due in printed and electronic form, and in poster form for presentation in class.

Peter G. Doyle 2012-05-23