Random numbers in matlab

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.

Answer 1

[Tom Lane]

Are you sure of the sqrt(N) result? I believe you would expect this if you took the square root of the average squared distance between b, the number in the first bin, and 10-b, the number in the second bin. But I haven't worked out the theoretical value for the average distance.

>> b = binornd(10,.5,1e6,1);
>> sqrt(mean((b-(10-b)).^2))
ans =
    3.1605
>> mean(abs(b-(10-b)))
ans =
    2.4583
>> sqrt(10)
ans =
    3.1623