i.i.d. Suppose Y,..., Yn ~ some continuous distribution with the following probability density function (PDF) with an unknown parameter 0 and support y > 0: 4 f(y|0) = 3ye, y >0. The mean of Y, is 0 and the variance of Y; is 02. (1) (5 points) Using the central limit theorem (CLT), find the approximate distribution for n(Y-30), where Y =Y. n (2) (5 points) Find the likelihood function of 0. Simplify as much as possible. (3) (5 points) Derive the MLE for 0 (denote it by MLE). (You don't need to check the 2nd derivative.) (4) (5 points) Calculate E(MLE) and Var( MLE). (5) (5 points) What does MLE converge to in probability? (Also state any theorem you used in solving this question.)