1. Maxwell. Sample y1, ...,Un; comes from Maxwell distribution with a density f (y|0) = 1 12 03 1 2 y ? e - 04 7 12, y 2 0, 0 > 0. Assume an exponential prior on 0, TT (0) = de-10, 0 > 0, 1 > 0. (a) Show that posterior belongs to gamma family and depends on data via E-, y?. (b) For A = 1/2 and y1 = 1.4, y2 = 3.1, and y3 = 2.5, find Bayes estimator for 0. How the Bayes estimator compares to the MLE and prior mean. The MLE for O is = = 3/y. (c) Using MATLAB/Octave/R/Python to calculate the 95% equitailed credible set for 0. (d) Find a prediction for a future single observation. For this, you will need the mean of Maxwell, which is E[Y] = 2 3