CIS 261 Fall 2019
Probability, Stochastic Processes, and Statistical Inference
Course Information
Course Description:
Instructors:
Name: | E-Mail: | Office: | Office Hours: |
Adam Zheleznyak | azhel@sas.upenn.edu |
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Class Schedule:
Preliminary Examination Schedule:
Weekly Quizzes:
Examination Policy:
Written Assignments Policy:
Grading Policy:
Texts:
CIS 261 Course Topics:
An Axiomatic Approach to Measure and Probability Spaces; The Generation of Finite Sigma-Fields via Finite Partitions; The Generation of Countable and Nondenumerable Sigma-Fields; Lebesgue Measure and Nonmeasurable Sets; The Properties of the Probability Function; The Definition of Conditional Probability; Bayes' Theorems; The Polya Urn Scheme; Independent Events; Product Probability Spaces; Important Discrete Probability Laws; An Axiomatic Derivation of the Poisson Probability Law; Important Continuous Probability Laws; The Cantor Distribution; Discrete and Continuous Random Variables; Univariate and Joint Point-Mass Functions; Univariate and Joint Cumulative Distribution Functions; Univariate and Joint Density Functions; Independent Random Variables; Functions of One or More Random Variables; Conditional Univariate and Joint Point-Mass Functions; Conditional Univariate and Joint Cumulative Distribution Functions; Conditional Univariate and Joint Density Functions; Conditioning With Respect to a Sub-Sigma-Field; The Lebesgue Integral; The Definition of the Expected Value of a Random Variable; The Fourier Transform and the Characteristic Function; The Variance of a Random Variable; The Expected Value of a Function of One or More Random Variables; The Definition and Properties of Conditional Expectations; Uncorrelated Versus Independent Pairs of Random Variables; Convergence Concepts for a Sequence of Random Variables; The Laws of Large Numbers; Central Limit Theory; The Definition of a Stochastic Process; The Normalized Wiener Process; The Levy Oscillation Theorem; The Ito Stochastic Integral; Parameter Estimation Techniques and Their Properties.