Mathematical statistics is the application of mathematics to study statistics using probability theory, linear algebra, measure theory, and stochastic analysis.

## Topics in Mathematical Statistics

Typical topics covered in a course [1]:

- Bivariate distributions
- Combinatorics and basic set theory notation
- Discrete distributions and continuous distributions
- Conditional probability
- Confidence Intervals: definitions, duality with hypothesis tests
- Convergence of random variables: in probability, in distribution, almost sure
- Central Limit Theorem, Law of Large Numbers
- Estimation: bias, MSE, consistency, sufficiency, maximum likelihood, method of moments, MVUE,
- Hypothesis testing: significance level, power, Neyman-Pearson lemma, Likelihood ratio tests
- Probability definitions and properties
- Rao-Blackwell Theorem, Fisher Information
- Random variables, expectation, variance
- Univariate and bivariate transformations: Box Cox Transformation, Fisher Z transformation.

## References

[1] Mathematical Statistics Topics. Retrieved May 7, 2022 from: https://stat.oregonstate.edu/content/mathematical-statistics-topics