Let Zl, Z2,... ,Zn be independent standard normal random variables, and let(a) What is the...

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 ?

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(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.