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Probabilistic Systems Analysis and Applied Probability >> Content Detail



Recitations



Recitations

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This section contains problems that are solved during recitation and tutorial sessions in addition to weekly notes that give an overview of topics to be covered. During recitations, the instructor elaborates on theories, solves new examples, and answers students' questions. Recitations are held separately for undergraduates and graduates. During tutorials, students discuss and solve new examples with a little help from the instructor. Tutorials are active sessions to help students develop confidence in thinking about probabilistic situations in real time. Tutorials are not mandatory but highly recommended for students enrolled in the course.



Weekly Notes



WEEK #TOPICS
1Probability Models and Axioms (PDF)
2Conditional Probability and Baye's Rule (PDF)
3Discrete Random Variables, Probability Mass Functions, and Expectations (PDF)
4Conditional Expectation and Multiple Discrete RVs (PDF)
5Continuous RVs (CDF, Normal RV, Conditioning, Multiple RV) (PDF)
6Continuous RVs (Conditioning, Multiple RVs, Derived Distributions) (PDF)
7Derived Distributions, Convolution, and Transforms (PDF)
8Iterated Expectations, Sum of a Random Number of RVs (PDF)
9Prediction, Covariance and Correlation, Weak Law of Large Numbers (PDF)
10Weekly Notes
11Bernoulli Process, Poisson Process (PDF)
12Weekly Notes
13Markov Chains (Steady State Behavior and Absorption Probabilities) (PDF)
14Central Limit Theorem (PDF)



Recitations



SES #RecitationsSOLUTIONS
R1Set Notation, Terms and Operators (include De Morgan's), Sample Spaces, Events, Probability Axioms and Probability Laws (PDF)(PDF)
R2Conditional Probability, Multiplication Rule, Total Probability Theorem, Baye's Rule (PDF)(PDF)
R3Introduction to Independence, Conditional Independence (PDF)(PDF)
R4Counting; Discrete Random Variables, PMFs, Expectations (PDF)(PDF)
R5Conditional Expectation, Examples (PDF)(PDF)
R6Multiple Discrete Random Variables, PMF (PDF)(PDF)
R7Continuous Random Variables, PMF, CDF (PDF)(PDF)
R8Marginal, Conditional Densities/Expected Values/Variances (PDF)(PDF)#
R9Derivation of the PMF/CDF from CDF, Derivation of Distributions from Convolutions (Discrete and Continuous) (PDF)(PDF)
R10Transforms, Properties and Uses (PDF)(PDF)
R11Iterated Expectations, Random Sum of Random Variables (PDF)(PDF)
R12Expected Value and Variance (PDF)(PDF)
R13Recitation 13(PDF)
R14Prediction; Covariance and Correlation (PDF)(PDF)
R15Weak Law of Large Numbers (PDF)(PDF)
R16Bernoulli Process, Split Bernoulli Process (PDF)(PDF)
R17Poisson Process, Concatenation of Disconnected Intervals (PDF)(PDF)
R18Competing Exponentials, Poisson Arrivals (PDF)(PDF)
R19Markov Chain, Recurrent State (PDF)(PDF)
R20Steady State Probabilities, Formulating a Markov Chain Model (PDF)(PDF)
R21Conditional Probabilities for a Birth-death Process (PDF)(PDF)#
R22Central Limit Theorem (PDF)(PDF)
R23Last Recitation, Review Material Covered after Quiz 2 (Chapters 5-7)



Tutorials



SES #TutorialsSOLUTIONS
T1Baye's Theorem, Independence and Pairwise Independence (PDF)(PDF)
T2Probability, PMF, Means, Variances, and Independence (PDF)(PDF)
T3PMF, Conditioning and Independence (PDF)(PDF)
T4Expectation and Variance, CDF Function, Expectation Theorem, Baye's Theorem (PDF)(PDF)
T5Random Variables, Density Functions (PDF)(PDF)
T6Transforms, Simple Continuous Convolution Problem (PDF)(PDF)
T7Iterated Expectation, Covariance/Independence with Gaussians, Random Sum of Random Variables (PDF)(PDF)
T8Correlation, Estimation, Convergence in Probability (PDF)(PDF)
T9Signal-to-Noise Ratio, Chebyshev Inequality (PDF)(PDF)
T10Two Instructive Drill Problems (One Bernoulli, One Poisson) (PDF)(PDF)
T11Poisson Process, Conditional Expectation, Markov Chain (PDF)(PDF)
T12Markov Chains: Steady State Behavior and Absorption Probabilities (PDF)#(PDF)

 








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