https://www.chenk.top/en/tags/joint-distributions/Recent content in Joint Distributions on Chen Kai BlogHugoenFri, 23 Aug 2024 09:00:00 +0000https://www.chenk.top/en/probability-statistics/04-joint-distributions/Fri, 23 Aug 2024 09:00:00 +0000https://www.chenk.top/en/probability-statistics/04-joint-distributions/<p>Until now, every distribution we&rsquo;ve studied described a single quantity: one die roll, one waiting time, one measurement. But interesting problems involve relationships between variables. Does studying more hours predict a higher exam score? Are stock returns correlated across sectors? How does the sum of two random variables behave?</p> <p>Answering these questions requires <strong>joint distributions</strong> — the mathematical framework for describing multiple random variables simultaneously. This is where probability theory starts connecting directly to regression, multivariate statistics, and the high-dimensional spaces of machine learning.</p>