(See Chan et al XXXXXXXXXXShow that the following updating algorithm for computing the sample mean and variance is really just the Givens method for the simplest regression problem ( just a common...

(See Chan et al. 1983.) Show that the following updating algorithm for computing the sample mean and variance is really just the Givens method for the simplest regression problem ( just a common mean):

                       Ti = Ti−1 + yi and Si = Si−1 + (iyi − Ti) 2 /[i(i − 1)].

Show that it is equivalent to the following code:

           s=0.

           ss=0.

           do i=1,n

           d=(y(i)-s)/i

           ss=ss+(i-1)*(y(i)-s)*d

           s=s+d

           end do ! loop on i