Discrete Random Variables (DRV)

IB AA SL: core and optional content

Core: the distribution table, E(X), and Var(X) by the binomial model np(1−p) (SL route solution). Optional: the general E(X²) method for Var(X) used in the default solution.

There are \(3\) red balls and \(5\) blue balls in a bag. \(2\) balls are drawn from the bag with replacement.

Let \(X\) be the random variable of number of red balls drawn. Construct the probability distribution table for \(X\) and show that \(X\) is a discrete random variable. Find \(\mathrm{E}\left( X \right)\) and \(\mathrm{Var}\left( X \right)\).