Independence — Topic Summaries
AI-powered summaries of 10 videos about Independence.
10 summaries
The quick proof of Bayes' theorem
Bayes’ theorem can be justified with a short, purely mathematical identity built from how “AND” works in probability. For two events, A and B, the...
If You Do These Weird Things, Academia Is Calling You
A PhD isn’t a test of credentials so much as a match between personality and the daily grind of research: relentless uncertainty, long rabbit holes,...
Chi-Square Test
Chi-square test of association (also called chi-square test of independence or Pearson’s chi-square test) is used to check whether two categorical...
Probability Theory 22 | Conditional Expectation (given random variables)
Conditional expectation given a random variable turns “conditioning on an event” into a new random variable that updates uncertainty based on what...
Probability Theory 19 | Covariance and Correlation [old version]
Covariance and correlation are introduced as the core tools for measuring how two random variables move together—especially when they are not...
Probability Theory 9 | Independence for Events [dark version]
Independence in probability is the idea that learning one event gives no information about how likely another event is. Formally, event B should not...
Probability Theory 22 | Conditional Expectation (given random variables) [dark version]
Conditional expectation given a random variable extends the familiar idea of “averaging with information” from conditioning on an event to...
Probability Theory 13 | Independence for Random Variables [dark version]
Independence for random variables is defined by checking whether the events created from their values behave independently—then that property can be...
Probability Theory 19 | Covariance and Correlation
Covariance and correlation provide a way to quantify how two random variables move together—whether they tend to increase and decrease in tandem, or...
Probability Theory 19 | Covariance and Correlation [OLD dark version]
Covariance and correlation provide a quantitative way to measure whether two random variables move together—and how strongly that co-movement departs...