On Wednesday, March 20, 2013 3:45:21 AM UTC-7, Thomas Plehn wrote: > while(1) %Matlab code > > > > rr = rand(1,50); %sequence of 50 U(0,1) Values > > > > des = rand(1,50); %sequence of 50 U(0,1) Values > > > > diff = rr - des; > > > > %This are both decide statistics, a, b > > a = mean(rr); > > b = min(diff); > > > > disp(a-b); %their difference is nearly constant > > %but how is it distributed (mu,sigma) > > > > %and how does that depend on sequence length (n=50) > > > > %i think we can chose U(0,1) insted of U(a,b) without los of generality > > %(linear transformation of coordinates) > > > > end
In plain English, is the following a description of your problem? (Below, I have changed the notation, and assigned different symbols from yours. However, if I understand correctly what you want, the concepts are the same.)
We take two independent samples X = (X_1,X_2,...,X_n) and Y = (Y_1,Y_2,...,Y_n) from the distribution U(0,1). [n = 50 in your case.] You take the difference sequence Z = (X_1-Y_1, X_2-Y_2,...,X_n-Y_n) and compute a = mean(X), b = min(Z) = smallest of the differences X_i - Y_i. Finally, you look at D = a - b. You want the mean and variance of D, and maybe also the actual distribution.
You claim that D is "almost constant", by which I assume you do the above computations many times, using many different samples, and come up with results that differ by little.
Is all that a fair summary of what you are trying to say?