Part2) Random Variables - 30 points Consider a game which involves rolling three dice. Write the Ft code for the following. Using the rollDie function from the prob library, setup the sample space for this experiment with the probability space. For each of the following scenarios from a) through e), show the corresponding outcomes and the probability of that event. The sample outputs for b) are shown as example. a) The sum of the rolls is greater than 10. b) All the three rolls are identical. Sample Output for outcomes: X1 X2 X3 pr'obs 1 1 1 1 0.00463 44 2 2 2 0.00463 87 3 3 3 0.00463 130 4 4 4 0.00463 173 5 5 5 0.00463 216 6 6 6 0.00463 Sample Output for probability: [1] 0.02778 0) Only two of the three rolls are identical. d) None of the three rolls are identical. e) Only two of the three rolls are identical given that the sum of the rolls is greater than 10. f) Add a random variable to the sample space for the sum of the rolls. Show the marginal distribution of this random variable. Using this random variable, what is the probability that the sum of the rolls is greater than 10. 9) Add a random variable to the sample space for determining whether all the rolls are identical. Show the marginal distribution of this random variable. Using this random variable, what is the probability that all the rolls are identical. h) Add a random variable to the sample space for determining if only two out of the three rolls are identical. Show the marginal distribution of this random variable. Using this random variable, what is the probability that only two out of the three are identical. i) Add a random variable to the sample space for determining if none of the three rolls are identical. Show the marginal distribution of this random variable. Using this random variable, what is the probability that none of the three are identical