4) Consider the following experiment: We roll two dice. Let the events Es is the sum of the top faces is s. a) Compute each set Es b) Let us make the random variable X(Es) = s. List the chart of the random variable X. That is the table with X values on the left and probabilities on the right. c) Find Pr(X > 7) d) Consider a random variable Y as follows: Y= 1 IF Pr(X>7) AND Y= 0 otherwise. *** note this is a simple Bernoulli trial b(Y, Pr( X >7)) Let us make the Bernoulli trial of 20 successive repetitions of the simple Bernoulli trial Y. That is b(Y, Pr(X>7), 20) Determine the following information a) Pr(b(Y=18, Pr(X>7), 20)) b) Notice that the Bernoulli trial b(Y=k,Pr(X>7), 20) gives us the probability that if we roll two dice twenty times EXACTLY k times the sum of the faces on the two die is greater than 7. Find the following: The expected number of times that the faces will add up to a number greater than 7 in 20 trials of the Bernoulli variable. The variance of this distribution. ** Hint: We wish to calculate the following: E(b(Y,Pr(X>7), 20)) AND V(b(Y,Pr(X>7), 20))