Course Description

Discrete and continuous random variables, expectation, independence and conditional probability; binomial, Bernoulli, normal, and Poisson distributions; law of large numbers and central limit theorem.

Additional Requirements for Graduate Students:
Extra problems on weekly homework.

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Athena Title

Probability

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Prerequisite

MATH 2270 or MATH 2270H or MATH 2500 or MATH 2500E or MATH 3510 or MATH 3510H

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Semester Course Offered

Offered fall, spring and summer

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Grading System

A - F (Traditional)

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Student Learning Outcomes

• Students will be able to state and interpret the axioms of probability, conditional probability, and independence.
• Students will be able to identify general properties, and specific examples, of discrete and continuous random variables.
• Students will be able to state and interpret the concepts of expectation, conditional expectation, variance, and covariance.
• Students will be able to explain the laws of large numbers and the central limit theorem.

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Topical Outline

• Basic counting principles and combinatorial coefficients
• Sample spaces and axioms for probability
• Conditional probability, Bayes' formula, independent events
• Random variables and expectation, binomial distribution, Bernoulli and Poisson random variables
• Continuous random variables, expectation, variance; Normal random variables, other continuous distributions such as exponential, gamma, Cauchy, beta
• Jointly distributed random variables
• Properties of expectation, expectation of the sum of random variables, conditional expectation, variance, and covariance
• Limit theorems: Weak law of large numbers, strong law of large numbers, central limit theorem
• Additional topics, depending on the instructor, may include probabilistic coding theory or entropy

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Syllabus

Select Faculty / Instructor to download syllabus:   Zhang, Qing

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