3 Dinner A company team is going out for dinner, and because the team is so large, they go to a restaurant that serves lots and lots of different appetizers-21 of them, in fact. They 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. What is E [T]? b. Define D to be the sum of the 21 numbers, minus the value of the highest roll andthe 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) You can leave your answer in terms of t and other numerical terms. c. Assume that H tracks the value of the highest roll. What is P(H = 6)? d. Assume M tracks the median of the 21 numbers rolled. What is P(M = 6)?