Question: Suppose that a random variable X has the Beta(3, 5) distribution. Evaluate the third and fourth factorial moments of X. {Hint: Observe that E[X(X ñ 1)(X - 2)] = E[X(X - 1)2 - X(X - 1)] = E[X(X - 1)2 ] - E[X(X - 1)]. Write each expectation as a beta integral and evaluate the terms accordingly to come up with the third factorial moment. The other part can be handled by extending this idea.}