**Problem 214 of Prof. Kim's Notes**Let \( \Omega = \mathbb{R} \) and \( \mathcal{F} \) be the \(\sigma\)-algebra generated by \( A = \mathbb{Q} \) (i.e., \( \mathcal{F} = \sigma(\{\mathbb{Q}\}) \)).(a) Write explicitly all the sets belonging to \( \mathcal{F} \).(b) Characterize all the mappings \( X : \Omega \rightarrow \mathbb{R} \) that are random variables with respect to \( (\Omega, \mathcal{F}) \).

Answered: Let 2 = R and F be the o-algebra…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Let 2 = R and F be the o-algebra generated by A = Q (i.e., F = o({Q})). (a) Write explicitly all the sets belonging to F. (b) Characterize all the mappings X : 2 R that are random variables with respect to (2, F)