Hi, I'm trying to do a simple simulation: Take a total of N objects and partition them into two bins, with probability of going into each bin = 1/2. To do this, I generate a random number, using rand(1), a total of N times. If the random number is less than 0.5, I "put" the object in 1 bin, while if it is greater than 1/2, I put the object in another bin. The average number of objects in each bin should be N/2. Also, one can show that the average of the difference of the number of objects in the two bins is Sqrt(N). I wrote some simple code to this simulation, and I indeed see that the average number of objects in a single bin approaches N/2 very closely. However, when I look at the average of the difference of the number of objects, I get something slightly less than Sqrt(N). Is rand not accurate enough to capture the higher moments of the distribution accurately.
