Question: 1. Let Y1, Y2.... be a sequence of random variables (not necessarily independent) taking on the values 0 and 1. Let Sn = Y1 +

1. Let Y1, Y2.... be a sequence of random variables (not necessarily independent) taking on the values 0 and 1. Let Sn = Y1 + ...Yn.

(a) Represent P(Yn+1 = 1|Sn = s) in terms of the joint distribution of the Yi.

(b) Further refine the representation when all permutations of the Yi such that Sn = s have equal probability (i.e., the Yi are exchangeable).

(c) What is the conditional probability if the Yi are independent?

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