https://www.chenk.top/en/tags/random-variables/Recent content in Random Variables on Chen Kai BlogHugoenTue, 20 Aug 2024 09:00:00 +0000https://www.chenk.top/en/probability-statistics/02-random-variables/Tue, 20 Aug 2024 09:00:00 +0000https://www.chenk.top/en/probability-statistics/02-random-variables/<p>After building the axiomatic foundation in the previous article, you might feel like we spent a lot of time talking about sets and subsets. That&rsquo;s because we did. The machinery of events and sigma-algebras is necessary but austere — it doesn&rsquo;t give us a natural way to compute averages, measure spread, or fit models to data.</p> <p>The bridge between abstract probability and applied statistics is the <strong>random variable</strong>. Once we assign numerical values to outcomes, the entire toolkit of calculus — derivatives, integrals, series — becomes available. And with calculus comes the ability to characterize randomness through a small set of named distributions, each encoding specific assumptions about how the world generates data.</p>