BE 6453 - Probability Theory

Institution:

Polytechnic Institute of New York University

Subject:

Description:

The axiomatic definition of experiment and probability. Conditional probability. Bayes' Theorem, Notion of independence. Repeated trials. Bernoulli trials and their limiting forms. The concept of a random variable. Probability distribution and density functions. Probability mass functions. Examples of random variables: Normal(Gaussian), Poisson, Gamma, Exponential, Laplace, Cauchy, Rayleigh, etc. Bayes' Theorem revisited. Functions of one random variable and their density functions. Expected value of a random variable: mean, variance, moments, and characteristic functions. Two random variables: Joint distribution and joint density functions of two random variables, independence. One function of two random variables. Two functions of two random variables. Order statistics. Joint moments, Uncorrelatedness, orthogonality, joint characteristic function. Jointly Gaussian random variables. Conditional distribution and conditional expected values. The central limit theorem. The principle of maximum likelihood. Elements of parameter estimation. Maximum likelihood estimation for unknown parameters. Unbiased estimators and their variances. Co-listed as EL 6303. Prerequisites: Graduate status and MA 3012.

Credits:

3.00

Credit Hours:

Prerequisites:

Corequisites:

Exclusions:

Level:

Instructional Type:

Multiple

Notes:

Additional Information:

Historical Version(s):

Institution Website:

www.poly.edu

Phone Number:

(718) 260-3100

Regional Accreditation:

Middle States Association of Colleges and Schools

Calendar System:

Semester

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