Math 493 - Schedule
 

 

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Schedule

Schedule of topics: Math 493

Date Chapter       Description 
Sep 1       1.1       Introduction, simulations
Sep 3 1.1 More simulations, distribution functions

Sep 6 Labor Day! (no class)
Sep 8 1.2 Discrete distributions -> probability
Sep 10 2.1 Simulating continuous distributions

Sep 13 2.1, 2.2 Bertrand's paradox, density functions
Sep 15 2.2 Density function examples
Sep 17 2.2 Cumulative distribution functions, exponential distribution

Sep 20 2.2, 3.1 Infinite coin flips, permutations
Sep 22 3.2 Combinations, the binomial theorem
Sep 24 3.2 Bernoulli processes, binomial random variables

Sep 27 3.2 Hypothesis testing in Bernoulli processes
Sep 29 3.2 Inclusion-exclusion, derangements
Oct 1 3.2, 3.3 Derangements, riffle shuffle model

Oct 4 3.3 Riffle shuffles: Rising sequences and interleavings
Oct 6 Exam 1
Oct 8 3.3 Riffle shuffles: Variation distance

Oct 11 4.1 Conditional probability, Monty Hall
Oct 13 4.1 Independence of events
Oct 15 Fall Break! (no class)

Oct 18 4.1 Random variables, extended
Oct 20 4.1 Joint distributions and independence
Oct 22 4.1 Bayes' Theorem

Oct 25 4.2 Continuous conditional probability
Oct 27 4.2 Independence of continuous R.V.'s
Oct 29 5.1 Geometric, negative biomial, Poisson distributions

Nov 1 5.1, 5.2 More Poisson distribution
Nov 3 5.2 Functions of R.V.'s, how to simulate continuous R.V.'s
Nov 5 5.2 Normal random variables, and the idea of Central Limit Theorems

Nov 8 6.1 Expected value
Nov 10 6.1 Linearity of expectation applications
Nov 12 Exam 2

Nov 15 6.1, 6.2 Conditional expectation; Variance
Nov 17 6.2 Variance -> "extra weak LLN"
Nov 19 6.2, 6.3 Variance examples, Continuous expectation and variance

Nov 22 6.3 Expectation and variance of exponential and normal RVs
Nov 24 Thanksgiving! (no class)
Nov 26 Thanksgiving! (no class)

Nov 29 7.1 Discrete convolutions
Dec 1 7.2 Continuous convolutions
Dec 3 8.1 - 8.2 Chebyshev Lemma and Weak LLN

Dec 6 8.2, 9 LLN applications, CLT statement
Dec 8 9.1 Proof of binomial CLT
Dec 10 9.1 Ideas towards general CLT; Applications of CLT

Dec 20 Final exam   (6:00 pm - 8:00 pm)

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