Imagine that we roll a fair sixsided die and a fair foursided die {i.e., all sides have the same probabil ity). Let X1 and Y1 be the independent random variables representing the outcomes of those events respectively. Let S = X1 +2 1'1 be the sum of the outcome of the roll of the sixsided die and mo times the outcome of the roll of the foursided die. Please answer the following questions with appropriate working f justication. 1. What is the variance of 3, Le, what is V [S]? [1 mark] 2. Determine the probability distribution of S, i.e., the probability that S = {3, . . . ,14}. [1 mark] 3. What is the expected value of 33, Le, what is E [33]? [1 mark] 4. Calculate the approximate value of ]E [33] using the Taylorseries procedure discussed in Lecture 2. [2 marks] 5. Imagine that we roll a second fair sixsided die; call the outcome of this roll X2. What is the (impacted value of {X1 + 2Y1 + X92, i.e., what is E [(X1 + 2Y1 + X2)2]? [1 mark]