Add Bivariate Distributions lecture - #837
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Adds a new lecture introducing bivariate distributions, placed after fitting_distributions and before lln_clt in the Probability and Distributions part of the toc. Covers joint/marginal distributions (discrete and continuous), independence, covariance and correlation, ways joint distributions arise (independent components; Y = aX + b + U), the bivariate normal distribution, and a counterexample showing normal marginals don't imply joint normality. Moves to observed data using the Ames house price dataset already used in observed_distributions/fitting_distributions, fits a bivariate normal by the method of moments, and closes with a preview showing the bivariate normal's conditional mean coincides with the OLS line, handing off to simple_linear_regression. Built and rendered locally to verify execution and output. Co-Authored-By: Claude Sonnet 5 <noreply@anthropic.com>
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Summary
Adds a new lecture, Bivariate Distributions, placed after
fitting_distributionsand beforelln_cltin the Probability and Distributions part.The three existing lectures in that part (
prob_dist,observed_distributions,fitting_distributions) all treat one variable at a time. This lecture is a quick, elementary bridge to pairs of variables, aimed at applied readers, before the series moves on tosimple_linear_regression/mle.Contents
Y = aX + b + Uobserved_distributions/fitting_distributions, now looking at price vs. floor area jointly (hexbin/jointplot, sample correlation)simple_linear_regressionVerification
yfinancedownload in the exercise) standalone — clean run, no errorsjupyter-book build bivariate_dist.md— notebook executed successfully (8.15s), HTML rendered correctly<figure>/<figcaption>wrapper), per the manual's guidance that captioned figures insidesolutiondirectives break the PDF build{doc}links and a bibtex key, expected for a standalone single-page build outside the full toc/bibliography context🤖 Generated with Claude Code