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

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MA 2631 - Probability II for AS

4 lecture hours 0 lab hours 4 credits
Course Description
This course continues where MA 2630  ended.  In particular, topics of discussion will include continuous probability distributions such as the uniform, normal, exponential, gamma, beta, Cauchy, and Weibull distributions, both discrete and continuous joint probability distributions, and additional expectation results, such as moment-generating functions, that were not discussed in MA 2630 . (prereq: MA 2630 )
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
  • Understand and apply continuous probability distributions to appropriate probability situations
  • Understand, derive, and use continuous probability density functions, conditional probability density functions, marginal functions, and moment-generating functions
  • Understand, derive, and use continuous joint probability functions
  • Understand the meaning and relevance of and use measures of dispersion for continuous multi-variable probability distributions
  • Understand, calculate, and use covariance
  • Understand, calculate, and apply to correlation coefficient appropriate situations
  • Perform transformations of continuous random variables
  • Form and use linear combination of random variables with respect to calculation of probabilities and moments

Prerequisites by Topic
  • Multivariable calculus
  • Discrete random variables

Course Topics
  • 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
  • Continuous joint probability functions, joint probability density functions, and joint cumulative density functions
  • Conditional and marginal distributions and densities
  • Moments for the discrete and continuous joint functions considered
  • Joint moment-generating functions
  • Measures of dispersion for multi-variable probability distributions
  • Covariance
  • Correlation coefficients
  • Transformations of continuous random variables
  • Linear combinations of random variables including probabilities and moments

Coordinator
Dr. Yvonne Yaz



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