1. [25 pts] = (a) [8 pts] Find (i). E(B²|F9) and (ii). E(B₁₁|F9); here F9 o(Bx: x ≤ 9). (b) [8 pts] Consider [0, 7] and

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1 25 Pts A 8 Pts Find I E B F9 And Ii E B F9 Here F9 O Bx X 9 B 8 Pts Consider 0 7 And 1 (78.44 KiB) Viewed 32 times

1. [25 pts] = (a) [8 pts] Find (i). E(B²|F9) and (ii). E(B₁₁|F9); here F9 o(Bx: x ≤ 9). (b) [8 pts] Consider [0, 7] and let π = {to,..., tn} be a partition of [0, T] with || = maxke{1,...,n} Atk. Show 2 n Ε(Σ(ΔΒ) - T →0 as → 0. k=1 (c) [9 pts] Let X, G be integrable random variables (on a probabilistic space (N, G, P)), F a o-field contained in G, o(X) CF, and X G be integrable. Show E(X G|F) = X E(G|F) a.s.