Question: Establish the following recursion relations for means and variances. Let X-n and S2n be the mean and variance, respectively, of X1,...,Xn. Then suppose another observation,

Establish the following recursion relations for means and variances. Let X-n and S2n be the mean and variance, respectively, of X1,...,Xn. Then suppose another observation, Xn+i, becomes available. Show that
(a) X-n+l

(b) nS2n+1 = (n - 1)S2n + (n/n+1) {Xn+1 - x-n)2

n+1

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