(5 points) Suppose f(x) = (8 - w)x7-", 0

(5 points) Suppose (8 w)x7 w 0 < < 1, w < 8 is a density function for a continuous random variable X (a) Find E[X]. Write your answer in terms of w. (b) Let m E[X] be the first moment of X. Find the method of moments estimator for w in terms of m. (c) Find the method of moments estimate for w based on the sample data for X below: 0.2, 0.4, 0.85, 0.85, 0.3, 0.15, 0.4 Round your answer to 3 decimal places