STAT 401 - Assignment 7 Consider rolling a 6-sided die. The outcome of interest is the number of dots that appear on thetopside 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 tothe number of dots on the top side of the die when it comes to rest. Suppose the die is fair (each side isequally likely).Define the random variable X to be the amount you are rewarded after one roll. Answer the following questions (please show work)

1) What are the possible values the random variable, X, can take on?

2) Explicitly write out the probability mass function (pmf) for the random variable X.

3) Write out explicitly the cumulative distribution function (CDF) for the random variable X.

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

5) How much does the amount rewarded vary around the value obtained in part (4)?