Consider rolling a 6-sided die. The outcome of interest is the number of dots that appears on the topside when the die stops rolling. The possible outcomes are 1, 2, 3, 4, 5 & 6. Suppose we play the following game. Roll the 6-sided die, you are rewarded a dollar amount equal to the number of dots on the topside of the die when it comes to rest. Suppose the die is fair (each side is equally likely). Define the random variable X to be the amount you are rewarded after one roll.

What is the 'typical' amount rewarded when playing this game?

How much does the amount rewarded vary around the value obtained?