Question 3: x, y, standard normal, iid. You generate 10k pairs of {x,y}, delete those pairs with x+y>0, you are then left with a new set of {x,y}, with x+y<=0. 1. Are x and y in this new set still independent? 2. Is the correlation of the new {x,y} set positive, 0 or negative? Try to give an explanation that a college student could understand. 3. What is the value of the correlation? We prefer an analytical answer. If you are not able to get the analytical solution, then compute a numeric one using any computing language to get partial credit on this question.