HMC Math 151.
Probability
Spring 1998

Prof. Francis Su
Olin 280
x73616

su@math.hmc.edu

This course will introduce you to the theory of probability and its applications. A sampling of things we will encounter: probability axioms, sample spaces, conditional probability, Bayes' formula, discrete and continuous random variables, expectation, variance, joint distributions, laws of large numbers, central limit theorem, Markov chains. We shall treat other topics as time permits.
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Weekly office hours:

Tuesdays 4-5:30 pm
or by appt.

Text: Ross, A First Course in Probability. We will cover Chapters 1-8 and from time to time treat supplemental topics not in the book.

Coursework: weekly problem sets (15-20 problems), posted Fridays on the web page and due Wednesdays in class. Do not wait until Tuesday to begin your assignment! Working together is OK, but write up problem solutions separately. Midterm I (take-home) on Friday, Feb. 20. Midterm II (take-home) handed out on Friday, April 3.

Grading: HW and 2 midterms worth 1/5 each, final worth 2/5. Lowest homework score dropped. Graders: Ryan Gatti and Kevin Watkins.

Honor Code: The HMC honor code applies in all matters of conduct concerning this course.

HW #1
due Wed 1/28
READ Chapters 1 and 2

DO
p.16 ( 1, 3, 4, 5, 6, 8ac, 11, 18, 21, 22, 26 )

p.19 ( 8, 9, 11 )

p.54 ( 2 )

HW #2
due Wed 2/4
READ Chapters 2 and 3

DO
p. 17 ( 13 )

p. 21 ( 12a )

ADDITIONAL PROBLEM:
Now prove the result of 12a in a different way,
using the binomial theorem on (x+1)^n, and differentiating.

p. 54 ( 3, 4, 5, 8, 9, 12, 15, 18, 22, 33)

p. 62 ( 6abdh, 11 )

HW #3
due Wed 2/11
READ Chapter 3

DO
p. 59 ( 28, 37, 53 )

p. 104 ( 1, 4, 8, 9, 10, 12,
         13, 14, 18, 22, 28, 31)

HW #4
due Wed 2/18
READ Chapter 4

DO
p. 106 ( 23, 50, 51, 53, 60
         61, 62, 72, 76 )

p. 120 ( 13, 16 )

p. 173 ( 4 )

TAKE-HOME EXAM due Monday, no HW for Wed 2/25
HW #5
due Wed 3/4
READ Chapter 5

    DO
    p. 174 ( 14, 21, 31, 35, 37,
             38, 39, 41, 42, 49,
             52, 56, 58, 60, 61, 66

    p. 185 ( 9, 20 )

HW #6
due Wed 4/1
READ Chapter 5

    DO
    p. 181 ( 51, 63, 69, 70, 73, 74 )

    p. 187 ( 13, 25, 33 )

    p. 232 ( 1, 2, 3, 7, 11, 13 )

HW #7
due Wed 3/25
READ Chapter 6

    Note this assignment is a bit shorter so you can have a more relaxing spring break!

    DO

    p. 232 ( 4, 15ab, 18, 24, 30, 32, 36 )

    p. 237 ( 4 )

HW #8
due Wed 4/1
READ Chapter 6

    DO

    p. 232 ( 8, 12, 16, 17, 19,
             20, 23, 25, 26, 27,
             37, 38)

    p. 239 ( 19, 20 )

    p. 293 ( 2, 10 )

HW #9
due Wed 4/15
READ Chapter 7.1-7.3

SHORTENED (yay!) !!!! ( 4/13/98)

    DO

    p. 293 ( 9abcd, 12, 16, 18,
             21, 27, 30, 33, 35, 49)

    p. 301 ( 4 [ see p.255], 14 )

HW #10
due Wed 4/22
READ 7.6 and Chapter 8

DO

p. 373 ( 5, 8, 16, 17,
           18, 32, 33 )

p. 391 ( 45, 50, 51 )