# Basic Elements of Probability Theory

## General

STAT

447

### College/School

College of Science and Engineering

### 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-dimensional variates, central limit theorem; T, F, and chi-square distributions.

3

3

No

No

No

## Learning Outcomes

### Outcome

Employ the concepts of sample space and event to calculate classical probabilities.

### Outcome

Apply tree diagrams, the law of total probability, and Bayes' rule to calculate conditional probabilities.

### Outcome

Define and use random variables.

### Outcome

Identify and examine typical distributions such as binomial, Poisson, geometric, hypergeometric, normal, uniform, gamma, beta, and exponential distributions.

### Outcome

Calculate marginal distributions and conditional distributions for a given joint distribution.

### Outcome

Calculate the mean, variance, quantiles, and moment generating function of a distribution.

### Outcome

Calculate the conditional mean and conditional variance of a distribution.

### Outcome

Use Jacobians to find distributions or joint distributions.

### Outcome

Distinguish basic sampling distributions such as normal, chisquared, t, and F distributions.

### Outcome

Apply typical distributions to solve real life problems.

## Dependencies

### Courses

STAT447 is a prerequisite for:

### Programs

STAT447 is a completion requirement for: