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Probabilistic Systems Analysis and Applied Probability >> Content Detail



Calendar / Schedule



Calendar

The calendar below provides information on the course's lecture (L), recitation (R), and tutorial (T) sessions.


Ses #TopicsKey Dates
L1Probability Models and AxiomsProblem set 1 out
R1Set Notation, Terms and Operators (include De Morgan's), Sample Spaces, Events, Probability Axioms and Probability Laws
L2Conditioning and Bayes' Rule
R2Conditional Probability, Multiplication Rule, Total Probability Theorem, Baye's Rule
L3IndependenceProblem set 1 due

Problem set 2 out
R3Introduction to Independence, Conditional Independence
T1Baye's Theorem, Independence and Pairwise Independence
L4Counting
L5Discrete Random Variables; Probability Mass Functions; ExpectationsProblem set 2 due

Problem set 3 out
R4Counting; Discrete Random Variables, PMFs, Expectations
T2Probability, PMF, Means, Variances, and Independence
L6Conditional Expectation; Examples
R5Conditional Expectation, Examples
L7Multiple Discrete Random VariablesProblem set 3 due

Problem set 4 out
R6Multiple Discrete Random Variables, PMF
T3PMF, Conditioning and Independence
L8Continuous Random Variables - I
R7Continuous Random Variables, PMF, CDF
L9Continuous Random Variables - IIProblem set 4 due

Problem set 5 out
R8Marginal, Conditional Densities/Expected Values/Variances
T4Expectation and Variance, CDF Function, Expectation Theorem, Baye's Theorem
L10Continuous Random Variables and Derived Distributions
Quiz 1 (Covers up to Lec #1-8 Inclusive)
T5Random Variables, Density Functions
L11More on Continuous Random Variables, Derived Distributions, Convolution
R9Derivation of the PMF/CDF from CDF, Derivation of Distributions from Convolutions (Discrete and Continuous)
L12TransformsProblem set 5 due

Problem set 6 out
R10Transforms, Properties and Uses
T6Transforms, Simple Continuous Convolution Problem
L13Iterated Expectations
R11Iterated Expectations, Random Sum of Random Variables
L13ASum of a Random Number of Random VariablesProblem set 6 due

Problem set 7 out
R12Expected Value and Variance
T7Iterated Expectation, Covariance/Independence with Gaussians, Random Sum of Random Variables
L14Prediction; Covariance and Correlation
R13Recitation 13
R14Prediction; Covariance and Correlation
L15Weak Law of Large NumbersProblem set 7 due

Problem set 8 out
R15Weak Law of Large Numbers
T8Correlation, Estimation, Convergence in Probability
Quiz 2 (Covers up to and Including Lec #14)
T9Signal-to-Noise Ratio, Chebyshev Inequality
L16Bernoulli Process
R16Bernoulli Process, Split Bernoulli Process
L17Poisson ProcessProblem set 8 due

Problem set 9 out
R17Poisson Process, Concatenation of Disconnected Intervals
T10Two Instructive Drill Problems (One Bernoulli, One Poisson)
L18Poisson Process Examples
R18Competing Exponentials, Poisson Arrivals
L19Markov Chains - IProblem set 9 due

Problem set 10 out
R19Markov Chain, Recurrent State
T11Poisson Process, Conditional Expectation, Markov Chain
L20Markov Chains - II
R20Steady State Probabilities, Formulating a Markov Chain Model
L21Markov Chains - IIIProblem set 10 due

Problem set 11 out

Problem set 11 due two days after Lec #21
R21Conditional Probabilities for a Birth-death Process
T12Markov Chains: Steady State Behavior and Absorption Probabilities
L22Central Limit Theorem
R22Central Limit Theorem
L23Central Limit Theorem (cont.), Strong Law of Large Numbers
R23Last Recitation, Review Material Covered after Quiz 2 (Chapters 5-7)
Final Exam

 








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