Suppose Y1, . . . , Yn i.i.d. some continuous distribution with the following probability density function (PDF) with an unknown parameter and support y > 0: f (y|) = 4 3 y2e 2y , y > 0. The mean of Yi is 3 2 and the variance of Yi is 3 4 2. (1) (5 points) Find the likelihood function of . Simplify as much as possible. (2) (5 points) Derive the MLE for (denote it by MLE). (You don't need to check the 2nd derivative.) (3) (5 points) Calculate E(MLE) and Var(MLE). (4) (5 points) What does MLE converge to in probability? (Also state any theorem you used in solving this