PROBLEM #3: Answer the following questions on point estimators. Show your work step by step. 3-a. 3-c. Let X denote the proportion of allotted time that a randomly selected student spends working on a certain aptitude test. Suppose the pdf of X is (3+1)x9. 0 S x S 1. 0, otherwise, f(x:9)={ where 1 0, where Am are two parameters and c is a certain positive constant. Construct a point estimator for A and 1;, respectively, by using either maximum likelihood estimation or methods of moments Let X and Y be independent random variables with the following probability density functions form = %e\"". and mm) = reW\". respectively, where 11,}: > 0. Denote Z and W as two random variables where Z = min(X,Y) and W takw the value 1 if Z = X and 0 if Z = Y. Given i.i.d observations (Zg, Wi), i = 1, - - - , 11, nd the MLEs of A and pr. Show your work