Find the smallest sigma-algebra for Ω = {−2, −1, 0, 1, 2}

Question

Find the smallest sigma-algebra for which the function X(ω)=2|ω| is a random variable. Ω = {−2, −1, 0, 1, 2}

Determine its distribution, probability function and E(X).

Answer 1

The smallest sigma algebra is S={Ω, ∅}

S = \{\{-2, -1, 0, 1, 2},\emptyset\}