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# University Catalog

### STAT 447. Basic Elements of Probability Theory

Credits: 3
 Department: Statistics Description: A more mathematical treatment of probability distributions than STAT 417. Probability concepts and laws; sample spaces, combinations and permutations, Bayes' theorem, discrete and continuous random variables, expected value, distribution of functions of random variables, two-demensional variates, central limit theorem; T, F, and chi-square distributions. Prerequisites: MATH 320 or MATH 321 Semester Offered: Fall Grading Method: ABCDF

#### Student Learning Outcomes

 1 Employ the concepts of sample space and event to calculate classical probabilities. 2 Apply tree diagrams, the law of total probability, and Bayes' rule to calculate conditional probabilities. 3 Define and use random variables. 4 Identify and examine typical distributions such as binomial, Poisson, geometric, hypergeometric, normal, uniform, gamma, beta, and exponential distributions. 5 Calculate marginal distributions and conditional distributions for a given joint distribution. 6 Calculate the mean, variance, quantiles, and moment generating function of a distribution. 7 Calculate the conditional mean and conditional variance of a distribution. 8 Use Jacobians to find distributions or joint distributions. 9 Distinguish basic sampling distributions such as normal, chisquared, t, and F distributions. 10 Apply typical distributions to solve real life problems.

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