2. Let xi ~ Rayleigh(o2) be n iid observations from a Rayleigh distribution with parameter 62 . (NOTE: the parameter of interest is of, and NOT o) Familiarize yourself with the Rayleigh distribution on Wikipedia. In R's standard packages, there is NOT code to evaluate the pdf and cdf of the Rayleigh distribution. a. Find the MLE of of analytically. b. Assuming that your data are as follows: X1 = 8.1, X2 = 5.4, X3 = 1.8, x4 = 2.9 Give the MLE for o2 c. Now using the same four data points, approximate the MLE numerically using "optim" in R. For this problem, since there is NOT a "drayleigh" function in R, you will need to write some R code that directly evaluates the loglikelihood