Jan 28, 2023  
2021-2022 Undergraduate Academic Catalog 
    
2021-2022 Undergraduate Academic Catalog [ARCHIVED CATALOG]

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MA 2630 - Probability I for AS

4 lecture hours 0 lab hours 4 credits
Course Description
This course introduces elementary probability theory, which includes basic probability concepts such as counting, sets, axioms of probability, conditional probability and independence, Bayes’ theorem, discrete random variables, common discrete distributions, joint distributions, properties of expectation, moment generating functions, and limit theorems. (prereq: sophomore standing in AS program or consent of instructor)
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
  • Perform basic set theory operations including union, intersection, and apply them to probability situations
  • Understand the differences between mutually exclusive events and independent events and apply this knowledge to probability situations
  • Understand the differences and similarities of combinations and permutations and how combinations are used to evaluate probabilities
  • Understand the concept of conditional probability and how it extends to the Law of Total Probability and Bayes’ Rule
  • Use various discrete probability distributions to determine probabilities
  • Use, understand, derive and use discrete probability mass functions, distribution functions, and moment-generating functions
  • Understand, derive, and use discrete joint probability functions
  • Understand the meaning and relevance of variance and standard deviation and how it relates to probability calculations
  • Understand and use the results of the Central Limit Theorem
  • Use a transformation function to transform one probability mass function into another

Prerequisites by Topic
  • Algebra
  • Calculus

Course Topics
  • Union and intersection notation, theory, and examples
  • Mutually exclusive events and independent events
  • Addition and multiplication rules for probability
  • Combinatorics
  • Conditional Probability
  • Law of Total Probability
  • Bayes’ Rule
  • Discrete probability distributions such as the binomial, Poisson, negative binomial, uniform, geometric, hypergeometric, etc.
  • Discrete probability mass functions
  • Discrete cumulative distribution functions
  • Discrete moment-generating functions
  • Continuous probability distributions such as the Gaussian (normal) distribution, Student-t, chi-squared, F, exponential, gamma, beta, etc.
  • Continuous probability density functions
  • Continuous cumulative density functions
  • Continuous moment-generating functions
  • Measures of dispersion (including variance)
  • Transformations of random variables

Coordinator
Dr. Yvonne Yaz



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