- #1
nasshi
- 18
- 0
The definition I have for a random variable is
[tex]X=\lbrace \omega \in \Omega \vert X(\omega) \in B \rbrace \in F[/tex] where F is a sigma algebra and B is a Borel subset of R.
Using function composition, how would one write a similar set notation definition for f(X), where f is a Borel measurable function?
[tex]f(X)=\lbrace \omega \in \Omega \vert f(X(\omega)) \in B \rbrace \in \sigma(X)[/tex] where [tex]\sigma(X)[/tex] is a sigma algebra and B is a Borel subset of R??
[tex]X=\lbrace \omega \in \Omega \vert X(\omega) \in B \rbrace \in F[/tex] where F is a sigma algebra and B is a Borel subset of R.
Using function composition, how would one write a similar set notation definition for f(X), where f is a Borel measurable function?
[tex]f(X)=\lbrace \omega \in \Omega \vert f(X(\omega)) \in B \rbrace \in \sigma(X)[/tex] where [tex]\sigma(X)[/tex] is a sigma algebra and B is a Borel subset of R??