Calculate and graph an approximate density function for the "Random Number Generator" (divide the interval (0,1) in 20 equal segments and then compute the relative frequency of each interval. Does the approximation converge to the true expected values? if so, how fast? Define and explain how do you measure the error (norm). How many trials are required for a specific precision? How does it scale with the number of trials? How would you run a test using the data in your two dimensional Poincare plot? What do you expect to find?
Please show all steps and explain (if you can post pictures of the plot and the commands, you'll get the full credit.)