Problem I (50pts): In this problem, let us consider a random experiment of dice-tossing. We assume that each die is a fair one with 1~6 dots shown on its sides. Our observation of the outcome of a die tossing is recorded as a number (a random variable). If we toss two dice simultaneously and record the outcome as ( X,, X", ), find the followings: 5. Find the expected values, E { X] ) =?, E(X,) =? 6. Find and sketch the probability mass function of the "summation", or, the summation random variable X, = X, + X2 . That is, P. (k) = P(X, + X, = k) vs. k 7. Find the expected value, E { X,. } =? 8. Find and sketch the probability mass function of the "difference", or, the difference random variable X X, - X, . That is, Por (k) = P(X, - X, = k) vs. k 9. Find the expected value, E X dig ) =