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The class covered fundamental probability concepts including the multiplication rule for independent events, complementary events, and the definition and application of random variables. The tutor and student also discussed the distinction between discrete and continuous random variables and introduced the concepts of probability mass functions and probability density functions.

The tutor administered a theoretical test covering topics in econometrics and statistics. The student demonstrated a solid understanding of concepts like dummy variables, heteroscedasticity, hypothesis testing at different significance levels, and weighted least squares. The next session will focus on practice problems similar to exam questions.

The class focused on econometric concepts, specifically addressing heteroskedasticity and omitted variable bias. The tutor and student worked through a problem involving the Breusch-Pagan-Godfrey test for heteroskedasticity and discussed methods for correcting it, such as robust standard errors and WLS. They also examined omitted variable bias in a wage regression model, identifying potential missing variables and solutions like proxy variables, instrumental variables, and fixed effects.

The Tutor and Student reviewed advanced calculus topics including Lagrange multipliers, Taylor series expansion, and Gaus-Jordan elimination. They practiced solving constrained optimization problems, finding Taylor series for given functions, and solving systems of linear equations and finding matrix inverses using Gaus-Jordan elimination. The session concluded with a discussion on finding critical points and classifying them using the second derivative test.

The tutor and student reviewed logarithmic linear regression and quadratic regression models, focusing on interpreting coefficients as percentage changes and understanding diminishing returns. They practiced applying these concepts to real-world examples involving wages and earnings, and solved various practice problems related to hypothesis testing, confidence intervals, and model evaluation metrics.

The student and tutor reviewed calculus and economic applications for an upcoming exam. They practiced identifying risk preferences, calculating gradients and tangent lines, finding critical points, performing Taylor series expansions, and solving constrained optimization problems using Lagrange multipliers. The session concluded with plans to review derivatives and Taylor series further and a final exam preparation check.