## Statistics I: Probability Theory & Statistical Inference - STA 505

### Course Objectives

The objectives of the course are to introduce the underlying concepts of probability and statistical inference. In particular, this course will provide a foundation in the underlying probability theory and distribution theory required for application of statistical inference. This theory will be built upon in STAT06 and other later courses. It is expected that students will have a solid prerequisite foundation calculus before enrolling in this course.

### Course Topics

- Basic Concepts, Numerical Characteristics, Probability Set Functions
- Properties of Probability, Methods of Enumeration
- Random Variables, Probability Density Functions
- Distribution Functions, Mathematical Expectation
- Special Mathematical Expectations, Chebyshev's Inequality
- Correlation, Correlation Coefficient, Stochastic Independence
- Discrete Random Variables: binomial, multinomial, and Poisson distributions
- Continuous Random Variables: Gamma, Chi-Square, and Beta distributions
- Continuous Random Variables: Normal and Bivariate Normal distributions
- Sampling Theory, Transformations of Random Variables
- The t and F distributions, Order Statistics,
- Moment Generating Function Technique, distribution of the sample mean and variance
- Limiting Distributions, Stochastic Convergence
- Limiting Moment Generating Functions
- Central Limit Theorem

### Example Syllabus