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Suppose tlhat random variable X represents the outcome when an nsided fair die is rolled (i.e. each outcome is equally likely to occur). The p.m.f. of X is then p(:c,-) = E where m = i for 1 S i S n. " . n(n + 1) a. Determine E[X] (the expected value of X) in a simplified form. [Hint: 22 = T] i=1 " n n + 1 2n + 1 b. Determine V(X) (the variance in X) in a simplied form. [Hint: 22'2 = #1 i=1 c. Suppose that the fair die has n = 7 sides. i. Use the results in parts (a) and (b) to nd the mean and variance of X. ii. Find the moment generating function MX(t) and use it to verify the results in part (c)(i)