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?
did not even notice second link, which is the more statistically accurate way of approaching the problem. And yes, almost every distribution becomes normal when you average them...however there are a few rare exceptions, that will never normalize.