Problem#2. A small rental franchise keeps detailed records of vehicles being returned damaged. In one year, 540 out of 3000 automobiles and 280 out of 2000 trucks were returned damaged. A total of 4180 vehicles were not returned damaged. Are type of vehicle and damaged/undamaged statistically independent events? (5 points) Tip: Perform the test of independence. Constructing a contingency table may also help. Problem #3. For each of the following, state whether the events created are mutually exclusive and whether they are collectively exhaustive. So, for each item below, you are expected to provide two answers: (1) whether mutually exclusive or not, and (2) whether collectively exhaustive or not. (8 points total; 2 pts each item) a. Undergraduate business students were asked whether they were sophomores or juniors. b. Each respondent was classified by the type of car he or she drives: sedan, SUV, American, European, Asian or none. c. People were asked, "Do you currently live in (i) an apartment or (ii) a house?" d. A product was classified as defective or not defective