The standard equations for computing the mean and covariance from N samples is

N=N1i=1Nx(i)

N=N1(x(i))N)(x(i)N)T

The direct implementation of these equations would require two passes through the data, once to computeN and once to computeN . However, sometimes this isn't possible or convenient. For instance, ifN is very large or the data is streaming in and can't be stored. In those cases we would like a recursive form of the equations so that we can computeN andN fromN1 and N1.

Prove that the mean vector can be updated asN=N1+N1(x(N)N1)