Question: 5.10 Let X be a random variable on the probability space (, , P). Let a set A with P(A) = 0

5.10 Let X be a random variable on the probability space (Ω, ℱ , P). Let a set A ∈ ℱ with P(A) = 0 and the sigma algebra generated by the set denoted σ(A).

What is E[X | σ(A)]? Let 1A denote the indicator of A. What is E[X | 1A]?

Comment: I have been given this question in an industry job interview. The problem is flawed in the sense that the answer may be given only if X is independent of 1A.

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