Suppose X has the moment generating function Mx(t) = (1 - 2t)-1/2 for t < 1
Find the first and second moments of X. That is, find E(X) and E(X²).
(5) (5 points) In Homework 6, you have shown that for X ~U(a, b), the expectation and variance of X are given by
1 1 (a+b) and Var(X) = (b−a)2 E(X) = (a+b)
In this problem, we let X ~ U(0, 1).
(a) Compute the moment generating function for X ~U(0, 1).
(b) Use the moment generating function to show that 1 E(X) = and Var(X) = 1/2 2 hence verifying the conclusion obtained in the previous homework.