Worked Example 1

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 \(\mathrm{Var}\left( X \right)\).