MATH 151  Introduction to Probability Theory
Winter quarter, 2015
Instructor: Amir Dembo
Office: Sequoia 129
Office Hours: W 12:001:00
or email
Course assistant: Jafar Jafarov
Office: 380380U1
Office Hours: F 11:001:00; Th 3:005:00
or email
Scope and Aim:
A first course in probability theory, similar in content
to STAT116, but with more emphasis on mathematical
foundations and analytical manipulations.
Material covered: Probability spaces as models for uncertainty,
and introduction to the corresponding mathematical analysis.
Combinatorial analysis for discrete spaces (binomial, Poisson,
geometric). Conditional probabilities and stochastic independence.
Random variables and expectation. Law of large numbers, Normal and
Poisson approximations. Continuous spaces (normal,
exponential, uniform) and densities.
Prerequisite:
Maturity in analysis, reflected by passing MATH52 at A
or higher grade, or the consent of instructor.
Meetings:
MWF 2:153:05, Herrin Hall (Biology), T195.
Text
Ross: A first course in probability, 9th edition, 2012 (you may use
the 8th or 7th editions, but be responsible for finding which
problem in your copy matches the assigned homeworks).
Alternative Text
Pitman: Probability, Springer Verlag, 1993;
See also
For applets and notes prepared by Susan Holmes
for teaching a similar class on the web click
Final exam:
(solution) : Monday, March 16, 12:153:15PM,
Herrin Hall, T195.
Material: 1.11.5,2.12.5,3.13.5,4.14.10,5.15.7,6.16.5,6.7,
7.2[without 7.2.17.2.2],7.47.5,7.7,7.8.1,8.28.3 of text.
The exam has 6 questions, each somewhat harder and longer
than an average homework problem.
You can bring to the exam your HWs,
their posted solution, a text book, your class notes and calculator.
Practice exam:
Try 3h timed solution of following 8 problems
from "SelfTest Problems" in textbook:
2.3,3.14(or 3.15),4.17(or 4.28),5.9(or 5.17),5.14,5.22(or 6.15),
6.9(or 6.12, or 7.25),7.4(or 7.27).
Alternatively, try 3h times solution of
Final 2014, then compare with its
solution.
Grading:
30% Homework
70% Final
Letter grade based on relative standing of the combined numerical work.
Homeworks:
Homework problems from text are due in class, Friday 2:15PM
on a weekly basis (about 10 problems/week, starting January 16).
Late homework will not be accepted (each correct homework
problem earns credit, so submit even partial solutions!).
See page 433 of text for final answer of most problems,
but to get homework credit you
must provide detailed derivations. Students may collaborate
in solving the homework, but should independently write
their own solutions.
Homework 1.40 denotes Problem 40 at the end of Chapter 1 of the text,
while 2.T.3 is Theoretical Exercise 3 at the end of Chapter 2, and so on.
Number of problems in each HW set will also be indicated in brackets below.
All homework solutions posted;
All graded works returned in class (by FRI 3/13, lecture).

HW1 due 1/16: 2.2,2.5,2.15,2.19,2.23,2.31,2.46,2.53,2.T.16[9]
(solution).

HW2 due 1/23: 3.14,3.23,3.28,3.41,3.44,3.60,3.67,3.74,3.90,3.T.7,3.T.30[11]
(solution).

HW3 due 1/30: 4.6,4.21,4.26,4.33,4.42,4.78,4.T.13,4.T.16,4.T.21,4.T.27[10]
(solution).
 HW4 due 2/6: 4.62,4.65,4.67,4.69,4.72,4.76,4.T.25,4.T.28,4.T.32,4.T35[10]
(solution).

HW5 due 2/13: 5.4,5.5,5.8,5.10,5.16,5.22,5.26,5.31,5.34,5.36[10]
(solution).
 HW6 due 2/20: 5.41,5.T.5,5.T.11,5.T.13,6.6,6.9,6.13,6.15[8]
(solution).

HW7 due 2/27: 6.16,6.18,6.20,6.22,6.24,6.25,6.28,6.31,6.T.8,6.T.11[10]
(solution).

HW8 due 3/6: 6.41,6.43,6.45,6.46,6.52,6.T.19,6.T.20,7.2,7.8,7.12,7.17[11]
(solution).

HW9 due 3/11: 7.25,7.26,7.42,7.44,7.48,7.53,7.69,7.72,7.75,7.T.10,7.T.11[11]
(solution).
Preliminary syllabus:
1/5 M(1.12.3) W(2.4;2.5) F(3.2;3.5)
1/12 M(3.3,3.4) W(3.4;4.1;4.2) F(4.34.6;4.9)
1/19 M() W(4.74.8.2) F(4.8.34.9)
1/26 M(4.10;5.1) W(5.2;5.3;5.5) F(5.2;5.3;5.5.1)
2/2 M(5.4;5.4.1) W(5.7;6.1;6.2) F(6.1;6.2)
2/9 M(6.3;5.6.1) W(6.3;6.4) F(6.4;6.5)
2/16 M() W(6.7) F(6.7;5.6.4)
2/23 M(7.2) W(7.4) F(7.5.1;7.5.2)
3/2 M(7.5.3;7.5.4) W(7.7) F(7.8.1;8.3)
3/9 M(8.3;8.2) W(5.6.25.6.4) F(Review)