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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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