Currently reviewing a lecture problem, it would be greatly appreciated if you answer fully, thank you!

E _ ' Let X be a random variable with probability density function f}; (or) given by fx[:r) = c(l 1'2) for |:r| g 1 and zero otherwise. a Evaluate the constant c b. Compute the cumulative distribution function of X. c. For any I: 13 11 compute EliX"). (1. Using your answer for part (c) , write the rst four terms in the Taylor series expansion of the moment generating function of X