Let Zl, Z2,... ,Zn be independent standard normal random variables, and let
(a) What is the conditional distribution of Sn given that Sk = y, for k = 1,..., n ?
(b) Show that, for 1≤ k ≤ n, the conditional distribution of Sk given that Sn = x is normal with mean xk/n and variance k(n — k)/n.
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