Hey everyone,

I hope, everyone is doing well. I would like to ask question about matlab's var built-in function.

I just generated uniformly distributed random signal using rand.

%% noisy signal generation   

 noise=rand(len,1)'; 

%% variance formula for uniformly distributed signal 
%% var(signal)=((l-k)(l-k+2))/12; 

    param=noise(end)-noise(1); 
    variance=((param*(param+2)))/12;

%% this is how matlab calculate the var function 
    RESID = noise - mean(noise);
    VAR = sum(RESID.*conj(RESID)) / len;

When I tried to execute the variance calculation manually, I got the different result compared to built-in function. Basically results are for variance=0.0023 and VAR=0.0847.

I know that rand function generates numbers randomly between 0 and 1. But this difference is normal? Matlab built-in function normalizes the result. Can we assume that formula for the variance calculation already somehow normalized? ( I am not sure this is accurate to say!)