Arial 11 + BIU AN CHEEZIE 71 17 1 1 12 . 1 1 3 1 4 1 1 1 5 1 1 1 6 1 1 . 7 1 1 . 8 . 1 1 9 . 1 10 . 1 11 . 1 12 1 . 13 1 . 14 1 15 . 1 16 Suppose you look at the cumulative average of each student for the entire student population of the University of Montreal. This population includes 45,000 students, of whom 6,000 are foreign students and 39,000 are domestic students. (a) [2 points] Is the cumulative mean expectation for the entire population an random variable? Is the expectation of the cumulative average conditional on the origin of the students (i.e., domestic or foreign) a random variable? Briefly justify your answers. (b) [2 points] Suppose that the expectation of the cumulative mean for the entire student population is 3.75 and the expectation of the cumulative mean for foreign students is 3.81. What is the expected cumulative mean for domestic students? Show your calculations. (c) [2 points] Consider again that the population of 45,000 students includes 6,000 foreign students and 39,000 domestic students. However, suppose now that the cumulative mean and the origin of the students (i.e., domestic or foreign) are independent random variables. Let us also assume that the expectation of the cumulative average of domestic students is 3.79. In this case, what would be the expectation of the cumulative mean for the entire population? Justify your answer. (d) [1 point] How would your answer to question (c) change if the population of 45,000 students had 8,000 foreign students and 37,000 domestic students instead? Justify your