6. In this problem, print and submit code and plots, together with written answers to the questions. (a) Use Python to simulate a standard normal random variable 10000 times and make a plot of the running average. That is, if X, is the ith simulated value, make a plot of n against n for n from 1 to 10000. Does this plot look like it converges to 0? (b) Consider the model described in class where a spinner is located one unit of distance away from an infinite wall. The angle Y that the pointer makes with the perpendicular to the wall is uniformly distributed over the interval (-/2, /2). The distance X of the point that the spinner points at to the perpendicular is thus Xtan Y. It was argued in class that X has no expectation (despite the fact that it might look as if it should have expected value 0). To illustrate this, use Python to simulate X 10000 times and make a plot of the running average of the simulated values. Does this plot look like it converges to 0? Does it look like it converges at all?