18.440 Probability and Random Variables
Spring 2007

Table

18.440 Spring 2007 Calendar 

Lecture Day and Date Topic Reading Due
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
W 2/7/07
F 2/9/07
M 2/12/07
W 2/14/07
F 2/16/07
T 2/20/07
W 2/21/07
F 2/23/07
M 2/26/07
W 2/28/07
F 3/2/07
M 3/5/07
W 3/7/07
F 3/9/07
M 3/12/07
W 3/14/07
F 3/16/07
M 3/19/07
W 3/21/07
F 3/23/07
M 4/2/07
W 4/4/07
F 4/6/07
M 4/9/07
W 4/11/07
F 4/13/07
W 4/18/07
F 4/20/07
M 4/23/07
W 4/25/07
F 4/27/07
M 4/30/07
W 5/2/07
F 5/4/07
M 5/7/07
W 5/9/07
F 5/11/07
M 5/14/07
W 5/16/07
W 5/23/07
Introduction
Combinatorics
Sample Space, Events, Axioms of Probability
Inclusion-Exclusion, Equally likely Outcomes, Paradox
Independent Events, Conditional Probability
Bayes' Rule
Conditioning events
Discrete Random Variables, PMF
Expected Value, Variance, Geometric, Pascal
Distributions: Bernouli, Binomial, Gaussian/Normal
Distributions: Poisson; Game Show Problem
Cumulative Distribution Function
Hypergeometric Random Variable; Match Problem
Continuous Random Variables, PDF
Review and Practice Test
Quiz 1
Distributions: Uniform, Gaussian/Normal
Distributions: Exponential
Functions of a R.V. and the Random Chord problem
Distributions: Erlang
Joint random variables
Independence and Conditional Distribution
Sums of Independent R.V.
Order Stats, Buffon's needle
Functions of Joint R.V., Stick Break Problem
Review and Practice Test
Quiz 2
Sample Mean, Sample Variance
Conditional Expectation, Interated Expectation
Conditional Variance
Moment Generating Functions
Correlations, Covariance; Random Sums of R.V.
Markov, Chebyshev, Chernoff Inequalities
Central Limit Theorem; Convergence of Distributions
Law of Large Numbers, Jensen's Inequality
Sequential Choice
Poisson Process
Markov Chains
Random Walks
Final Exam
 1.1-1.4
 1.5-1.6
 2.1-2.3
 2.4-2.6
 3.1-3.2
 3.3-3.4
 3.5
 4.1-4.2
 4.3-4.5
 4.6
 4.8
 4.7,4.9
 4.8.3
 5.1
 
Quiz 1
 5.2-5.4
 5.5.0
 5.7
 5.6.1
 6.1
 6.2
 6.3
 6.2, 6.6
 6.7
 
Quiz 2
 7,2, 7.4
 7.5-7.5.2
 7.5.4
 7.7
 7.7
 8.2, 8.5
 8.3-8.4
 8.4-8.5
 7.5.3
 9.1
 9.2
 
Final Exam
 
 
 
Problem Set 1
 
 
Problem Set 2
 
 
Problem Set 3
 
 
Problem Set 4
 
 
Quiz 1
 
 
Problem Set 5
 
 
Problem Set 6
 
 
Problem Set 7
 
Quiz 2
 
 
Problem Set 8
 
 
Problem Set 9
 
 
Problem Set 10
 
 
 
Final Exam