3. MOM and MLE Estimation Let X1, . .., Xn ~ fx(x) where: fx (x) = OSI

3. MOM Let Xl, and M LE Estimation , Xn f X (C) where: fx(c) 29 o, Suppose we observe four values: = (a) It turns out that E(X) where otherwise = 2.28 3.14.... Give the Method of Moments estimator for 9 and report the numerical estimate based on the four data values. (4 points) (b) The likelihood function is: L(9) = Le 29 i. Give the log-likelihood function Z(9) = (3 points) iir Take the derivative of Z(9) with respect to 9, set it equal to zero, solve for 9, and report the Maximum Likelihood estimator of 9. (Assume 2nd derivative test passes) (5 points) iii. Based of the four data values above, report the Maximum Likelihood estimate of 9. (2 points)