These quizzes explore what a discrete random variable really is, from basic definitions to probability density functions to joint distributions.

Out of a box with \(3\) red and \(3\) blue balls, one ball is selected uniformly randomly. Out of the remaining \(5\) balls, another ball is selected uniformly randomly. The random variable \(X\) takes value \(0\) if the first selected ball is red and \(1\) otherwise. The random variable \(Y\) takes value \(0\) if the second selected ball is red and \(1\) otherwise. Are \(X\) and \(Y\) independent random variables?