Project: Central Limit Theorem
The [[Central_limit_theorem#Classical_CLT|Central Limit Theorem]] states that if we take random samples of size N from any distribution of independent random variables, that the distribution of sample averages (`bar X`) should fall in a normal distribution regardless of the type of distribution of the samples. For example our typical random number generators use a uniform, not normal, distribution. But if we take samples of size N, average them, then we should get a sample distribution that is normal with a mean that is the same as our sample source distribution mean and a standard deviation that is equal to the standard deviation of our sample source distribution divided by `sqrt(N)`.
Write a program that accepts a sample size N on the command line and the number of samples to collect M. Then generate the mean (`bar X`) of a sample of size N from random float values [0, 20). Do this M times maintaining a running count of the occurances in an array of 20 by using `lfloor bar X rfloor` (use floor() or int() function) to select the array element to increment. Output a tab-delimited table with the array index in column 1 and the count in column 2. This output can easily be piped into the Histogram project to get a simple graph that should look like a normal distribution centered on 10.0. Notice how as the sample size increases, the standard deviation shrinks?