Chapter 8, Problem 62RE

Two fair (not weighted) dice are each numbered with a $3$ on one side, a $2$ on two sides, and a 1 on three sides. The dice are rolled, and the numbers on the two up faces are added. If $X$ is the random variable associated with the sample space $S=\left\{2,3,4,5,6\right\}:$

(A) Find the probability distribution of $X$.

(B) Find the expected value of $X$.