18.440 Probability and Random Variables: Fall, 2011
Lectures: MWF 1011, 34101
Office hours: Wednesday 122, 2180
TA: Benjamin Iriarte Giraldo
TA office hours: Thursday 46, 2333
Text: A First Course in Probability, 8th edition, by Sheldon Ross
Assignments: Homeworks (20%), midterm exams (40%), final exam (40%)
Stellar course web site
TENTATIVE SCHEDULE

Lecture 1 (September 7): 1.11.3 Permutations and
combinations
(also Pascal's
triangle  as
studied (not invented) by Pascal, see also
correspondence with Fermat.
)
 Lecture
2 (September 9): 1.41.5 Multinomial coefficients
and more
counting (see
Pascal's pyramid)
Problem Set One, due September
16

Lecture 3 (September 12): 2.12.2 Sample spaces and set
theory

Lecture 4 (September 14): 2.32.4 Axioms of probability (see
Paulos' NYT article and a famous hat
problem)
)

Lecture 5 (September 16): 2.52.7 Probability and equal likelihood
(and a bit more
history )
Problem Set Two, due September
23

Lecture 6 (September 19): 3.13.2 Conditional probabilities

Lecture 7 (September 23): 3.33.5 Bayes' formula and independent
events
Problem Set Three, due
September
30

Lecture 8 (September 26): 4.14.2 Discrete random variables

Lecture 9 (September 28): 4.34.4 Expectations of discrete random
variables (and, for nondiscrete setting, examples of nonmeasurable sets,
as in the Vitali construction)

Lecture 10 (September 30): 4.5 Variance
Problem Set Four, due
October 7

Lecture 11 (October 3): 4.6 Binomial random variables, repeated
trials and the socalled Modern Portfolio Theory.

Lecture 12 (October 5): 4.7 Poisson random variables

Lecture 13 (October 7): 9.1 Poisson processes
Problem Set Five, due October
14

Lecture 14 (October 12): 4.84.9 More discrete random variables

Lecture 15 (October 14): 5.15.2 Continuous random variables
Practice Midterm Exam
with partial solutions (here is an old
midterm
and 2009 Midterm One With
Solutions
)

Lecture 16 (October 17): 5.3 Uniform random variables

Lecture 17 (October 19): 5.4 Normal random variables

Lecture 18 (October 21): REVIEW

Lecture 19 (October 24): FIRST MIDTERM: See
Spring
2011 MIDTERM EXAM
on CHAPTERS 14 (plus 5.15.4
and 9.1) with
solutions .
Fall
2011 MIDTERM EXAM
on CHAPTERS 14 (plus 5.15.4
and 9.1) with
solutions .

Lecture 20 (October 26): 5.5 Exponential random variables

Lecture 21 (October 28): 5.65.7 More continuous random variables
Problem Set Six, due November
4

Lecture 22 (October 31): 6.16.2 Joint distribution functions

Lecture 23 (November 2): 6.36.5 Sums of independent random
variables

Lecture 24 (November 4): 7.17.2 Expectation of sums
Problem Set Seven, due
November 9

Lecture 25 (November 7): 7.37.4 Covariance

Lecture 26 (November 9): 7.57.6 Conditional expectation
Practice Midterm Exam Two
with
partial solutions and 2009 Midterm Two
with solutions
.

Lecture 27 (November 14): 7.77.8 Moment generating distributions

Lecture 28 (November 16): REVIEW

Lecture 29 (November 18): SECOND MIDTERM: See
Spring 2011 Second midterm exam on 17 (plus 9.1) with
solutions.
FALL 2011 SECOND MIDTERM SOLUTIONS
Problem Set Eight, due
November 23

Lecture 30 (November 21): 8.18.2 Weak law of large numbers

Lecture 31 (November 23): 8.3 Central limit theorem
Problem Set Nine, due December
2

Lecture 32 (November 28): 8.48.5 Strong law of large numbers (see
also
the truncationbased proof on Terry Tao's blog and the characteristic
function proof of the weak law) and Jensen's inequality.

Lecture 33 (November 30): 9.2 Markov chains

Lecture 34 (December 2): 9.39.4 Entropy
Problem Set Ten, due December
9
(plus
martingale note)

Lecture 35 (December 5): Martingales and the
Optional Stopping Time
Theorem
(see also prediction market plots)

Lecture 36 (December 7): Risk Neutral Probability and BlackScholes
(look up options quotes at the Chicago Board Options Exchange)

Lecture 37 (December 9): REVIEW

Lecture 38 (December 12:) REVIEW

Lecture 39 (December 14): REVIEW
Practice Final with
partial solutions
 December 19:
Final exam
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