CIS 261 Fall 2017

Probability, Stochastic Processes, and Statistical Inference

Course Information

Course Description:

Instructors:

  • Teaching Assistants:

    Name: E-Mail: Office: Office Hours:
    Austin Gwiazdowski gwiazdowski.austin@gmail.com

    TBA

    TBA

    Michael Plumb mplumb@sas.upenn.edu

    TBA

    TBA

    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.