- #1
ellese
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I have this homework question and I'm a little bit stuck.
The question is:
Let (Ω, F , P ) be the unit interval probability space, and X be the random variable
defined by
(See attatchment)
Find the σ-algebra generated by X.
From my understanding of sigma-algebras I want to look for the set that is non-empty, closed under complementation and closed under countable unions.
The idea I have so far is to include the sets {1}{3} and {(3, 7]} but I'm not sure how to combine these into a sigma algebra. Do I want σ(X) = {∅, {1}{3}{(3, 7]}{[3,7]}, {1, (3,7]}, {1, 3} , {1, [3,7]}}?
The question is:
Let (Ω, F , P ) be the unit interval probability space, and X be the random variable
defined by
(See attatchment)
Find the σ-algebra generated by X.
From my understanding of sigma-algebras I want to look for the set that is non-empty, closed under complementation and closed under countable unions.
The idea I have so far is to include the sets {1}{3} and {(3, 7]} but I'm not sure how to combine these into a sigma algebra. Do I want σ(X) = {∅, {1}{3}{(3, 7]}{[3,7]}, {1, (3,7]}, {1, 3} , {1, [3,7]}}?