Statistical Learning - C$507 Madjid Allili ~ Johnson 125 ~ ext. 2740 ~ malliliQubishops . ca Homework #2: Due on 02/16/2023. 1. You must work in groups of 4 or 5 people. Submit one copy for each group with all the names clearly written on the front page. Justify concisely all your answers! 2. Name the submitted file as: Homework2-LastName-FirstName, where the Last Name and FirstName should correspond to the last name and the first name of the person who submits the file. 1. Let X1, X2, X3. ...;Xx denote a random sample of size n from a population whose density is given by f(x10) = Be-210 a >0, 0 elsewhere, where 0 is unknown. Consider the estimator of 0 given by O = min(X]. . .., X,). (a) Show that O is a biased estimator for 0. (b) Find a multiple , of O that is an unbiased estimator of 0. (c) Find MSE(@,). 2. Consider the independent observations 21, 12,..., I'm from the shifted exponential dis- tribution with pdf f(x10) = I > 0, else. (a) Show that 0 does not admit a MLE estimator. (b) Explain why we can redefine the pdf of the shifted exponential as x20, (1) else. without incidence on the distribution. (c) Use formula 1 as the pdf of the shifted exponential to find maximum likelihood estimator of the parameter 0