The course staff is going out to dinner next week to celebrate, and because the staff is so large and everyone's palates so varied, we've converged on a restaurant that serves lots and lots of different appetizers-21 of them, in fact. Of course, being the probability geeks we are, we plan on rolling a fair, 6-side die 21 times to determine how many servings of each appetizer to order. To put all this in more formal terms, we'll let the total number of servings across all appetizers be modeled by a random variable T which takes on whatever value you get when the 21 independent die rolls are added together. Your final answers should not be in terms of random variables. a. Define D to be the sum of the 21 numbers, minus the value of the highest roll and the value of the lowest roll. What is E[D]? (Hint: there's an easy way to derive the result without a lot of algebra.) Let t be your answer to part (a) (Answer E[T] = 21 = 3.5). You can leave your answer in terms of t and other numerical terms.