MATH 251 - Introduction to Mathematical Statistics (Calculus-based)

1. Apply probability calculations for various discrete and continuous probability distributions.
2. Apply the Central Limit Theorem.
3. Identify correct data collection techniques for use in both observational studies and experiments.
4. Identify correct data collection methods such as sampling surveys, experimental designs and observational studies;
5. Represent relationships between variables in graphical displays, use correlation and regression to explain such relationships;
6. Formulate and solve problems involving uncertainty using both experimental and theoretical probabilities.
7. Construct and interpret confidence intervals and test hypotheses in a variety of contexts, using likelihood ratio tests, Rao-Blackwell Theorem, Neyman-Pearson, as appropriate.
8. Describe Bayesian methods and differences from classical methods.
9. Demonstrate appropriate use of technological tools for collecting, analyzing, and drawing conclusions from data;
10. Identify the misuse of statistics and common misconceptions of probability.
11. Use appropriate technology, including statistical software, to solve a variety of problems.
12. Use correlation, regression, and graphical displays to mathematically model real world data.

• Basic elements of probability to support statistics
• Concept of random variables and probability distributions
• Important distributions of both discrete and continuous types, including the binomial, hypergeometric, chi-square, normal, t, and uniform distributions
• Sampling distributions and Central Limit Theorem
• Descriptive statistics including numerical and graphical summaries of data
• Introduction to data collection methods including sampling designs, experimental designs and observational studies
• Inferential statistics, including confidence intervals and hypotheses tests
• Regression topics, including linear regression and correlation

 
Course Addendum - Syllabus (Click to expand)