6.041 | Spring 2006 | Undergraduate

# Probabilistic Systems Analysis and Applied Probability

## Calendar

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

Ses # Topics Key Dates
L1 Probability Models and Axioms Problem set 1 out
R1 Set Notation, Terms and Operators (include De Morgan’s), Sample Spaces, Events, Probability Axioms and Probability Laws

L2 Conditioning and Bayes’ Rule

R2 Conditional Probability, Multiplication Rule, Total Probability Theorem, Baye’s Rule

L3 Independence Problem set 1 due

Problem set 2 out

R3 Introduction to Independence, Conditional Independence

T1 Baye’s Theorem, Independence and Pairwise Independence

L4 Counting

L5 Discrete Random Variables; Probability Mass Functions; Expectations Problem set 2 due

Problem set 3 out

R4 Counting; Discrete Random Variables, PMFs, Expectations

T2 Probability, PMF, Means, Variances, and Independence

L6 Conditional Expectation; Examples

R5 Conditional Expectation, Examples

L7 Multiple Discrete Random Variables Problem set 3 due

Problem set 4 out

R6 Multiple Discrete Random Variables, PMF

T3 PMF, Conditioning and Independence

L8 Continuous Random Variables - I

R7 Continuous Random Variables, PMF, CDF

L9 Continuous Random Variables - II Problem set 4 due

Problem set 5 out

R8 Marginal, Conditional Densities/Expected Values/Variances

T4 Expectation and Variance, CDF Function, Expectation Theorem, Baye’s Theorem

L10 Continuous Random Variables and Derived Distributions

Quiz 1 (Covers up to Lec #1-8 Inclusive)

T5 Random Variables, Density Functions

L11 More on Continuous Random Variables, Derived Distributions, Convolution

R9 Derivation of the PMF/CDF from CDF, Derivation of Distributions from Convolutions (Discrete and Continuous)

L12 Transforms Problem set 5 due

Problem set 6 out

R10 Transforms, Properties and Uses

T6 Transforms, Simple Continuous Convolution Problem

L13 Iterated Expectations

R11 Iterated Expectations, Random Sum of Random Variables

L13A Sum of a Random Number of Random Variables Problem set 6 due

Problem set 7 out

R12 Expected Value and Variance

T7 Iterated Expectation, Covariance/Independence with Gaussians, Random Sum of Random Variables

L14 Prediction; Covariance and Correlation

R13 Recitation 13

R14 Prediction; Covariance and Correlation

L15 Weak Law of Large Numbers Problem set 7 due

Problem set 8 out

R15 Weak Law of Large Numbers

T8 Correlation, Estimation, Convergence in Probability

Quiz 2 (Covers up to and Including Lec #14)

T9 Signal-to-Noise Ratio, Chebyshev Inequality

L16 Bernoulli Process

R16 Bernoulli Process, Split Bernoulli Process

L17 Poisson Process Problem set 8 due

Problem set 9 out

R17 Poisson Process, Concatenation of Disconnected Intervals

T10 Two Instructive Drill Problems (One Bernoulli, One Poisson)

L18 Poisson Process Examples

R18 Competing Exponentials, Poisson Arrivals

L19 Markov Chains - I Problem set 9 due

Problem set 10 out

R19 Markov Chain, Recurrent State

T11 Poisson Process, Conditional Expectation, Markov Chain

L20 Markov Chains - II

R20 Steady State Probabilities, Formulating a Markov Chain Model

L21 Markov Chains - III Problem set 10 due

Problem set 11 out

Problem set 11 due two days after Lec #21

R21 Conditional Probabilities for a Birth-death Process

T12 Markov Chains: Steady State Behavior and Absorption Probabilities

L22 Central Limit Theorem

R22 Central Limit Theorem

L23 Central Limit Theorem (cont.), Strong Law of Large Numbers

R23 Last Recitation, Review Material Covered after Quiz 2 (Chapters 5-7)

Final Exam

## Course Info

Spring 2006
##### Learning Resource Types
Simulation Videos
Simulations
Problem Sets with Solutions
Exams with Solutions
Lecture Notes