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Question 1: Let X have a U(0,1) distribution. In other words, f(x) = 1 for x (0,1) and 0 otherwise. a. Find the MGF of

Question 1: Let X have a U(0,1) distribution. In other words, f(x) = 1 for x (0,1) and 0 otherwise. a. Find the MGF of X b. Find a general formula for the raw moments of X. In other words, find a formula for E(Xr) as a function of r. c. Find the fourth central moment 4 = E[(X )4]. Hint: expand the terms inside the expectation, and then use linearity of expectation and your result from part b).

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