This is an easy problem, but it has been awhile since I have done basic statistics. If anyone can refresh my memory, that would be greatly appreciated. I believe the answer to the second problem is 100, as they are related by squares...but I am not 100% sure.
Xi is the result of the ith run of a Monte Carlo simulation, i = 1, 2... 1000. Let the Xi be independent and identically distributed with mean 10-4 and variance 10-6.
(a) What is the standard deviation of Y, where Y is the average of the Xi?
(b) If we wish to reduce the standard deviation of Y by a factor of 10, how many additional simulation runs do we need to do, above and beyond the 1000 that we have already done?