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 |