This undergraduate-level course introduces 3rd-year mathematics students to key concepts in statistics and probabilistic simulations. Topics included simulation of random variables, estimation theory, confidence intervals, and hypothesis testing. For one of the student groups, I was responsible for leading tutorial sessions to practice exercises and for conducting computer lab classes to teach statistical inference using R.

Syllabus

• Simulation of real-valued random variables
• Law of Large Numbers, Central Limit Theorem, Markov and Chebyshev inequalities
• Statistical estimation: estimators, bias, convergence, quadratic risk
• Asymptotic properties and normal approximations
• Method of moments and maximum likelihood estimation
• Confidence intervals and hypothesis testing
• Introduction to R and fundamental tools for statistical inference