MTH (0144) 550 - Probability and Statistics

Credits: 3.00

Students explore advanced probability and statistics from the point-of-view of measure theory. Students will also explain expectation distributions, laws of large numbers, and central limit theorems. Additionally, students will be exposed to a theoretical treatment of statistical inference and will apply sufficiency, estimation, hypothesis testing, and nonparametric methods.

●   Apply the techniques of measure theory. This will be assessed by Quiz 1 and the mid-term examination.
●   Explain the measure-theoretic formulation of probability theory. This will be assessed by Quizzes 2 & 3, and the mid-term examination.
●   Explain the classical theory of sums of independent random variables: laws of large numbers. This will be assessed by the mid-term examination.
●   Explain technical topics relating to notions of convergence, a.s. convergence techniques. This will be assessed by the mid-term examination.
●   Apply conditional distributions and conditional expectations. This will be assessed by Quizzes 2 & 3, and the mid-term examination.
●   Explain unbiased estimation. This will be assessed by Quiz 4-6, and the mid-term examination.
●   Apply parametric estimation. This will be assessed by Quizzes 7 & 8, and the final examination.
●   Apply nonparametric estimation. This will be assessed by Quiz 9, and the final examination.
●   Apply hypothesis testing. This will be assessed by Quiz 10 and the final examination.