Problem 3: Let Ω be a sample space, and P a probability on Ω. Suppose that B1, B2, B3 are pairwise disjoint, have positive probability, and their union is Ω. We let G := σ (B1, B2, B3) .
For a fixed set A ⊂ Ω, suppose that we have P(A|G) = 12IB2. Here, IB2 denotes the
indicator function of the set B2.
(a). Show that the random variable Y := P (A | G) is G-measurable.
Let F := 2Ω (the power set of Ω), and let H := {∅,Ω}.
(b). Is Y F-measurable? Why?
(c). Is Y H-measurable? Why?
(It is an intro to math finance course problem)