Explain why the assumption is important problem 2 14

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Unformatted text preview: plain why the assumption is important. Problem 2 (14 pts). This problem deals with positive random variables that may get the value ∞. Let be a random variable defined on a probability space . Let ℱ⊂ be a σ-algebra. Prove a. (6 points) (i) ℱ (ii). ℱ and (Namely, we can write exist, and , ) ℱ ℱ b. (8 points) If is a random variable that satisfy (ii) of part a, namely: , ℱ then ℱ and Problem 3 (18 pts). Let be a sequence of integrable random variables defined on ℱ and let ℱ be an increasing seq...
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This document was uploaded on 03/01/2014 for the course STATS 400 at Michigan State University.

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