Difference between revisions of "Random variable"
From Maths
(Created page with "==Definition== A '''Random variable''' is a measurable map from a probability space to any measurable space {{Def...") |
m |
||
| Line 1: | Line 1: | ||
==Definition== | ==Definition== | ||
A '''Random variable''' is a [[Measurable map|measurable map]] from a [[Probability space|probability space]] to any [[Measurable space|measurable space]] | A '''Random variable''' is a [[Measurable map|measurable map]] from a [[Probability space|probability space]] to any [[Measurable space|measurable space]] | ||
| + | |||
| + | Let {{M|(\Omega,\mathcal{A},\mathbb{P})}} be a [[Probability space|probability space]] and let {{M|\Epsilon:\Omega\rightarrow\mathbb{R} }} be a random variable | ||
| + | |||
| + | (that means it is a [[Measurable map|measurable map]] '''FROM''' a probability space to a measurable space recall) | ||
| + | |||
| + | Then: | ||
| + | |||
| + | {{Todo|Finish this because it's iffy}} | ||
| + | |||
| + | |||
{{Definition|Measure Theory|Statistics}} | {{Definition|Measure Theory|Statistics}} | ||
Revision as of 20:03, 18 March 2015
Definition
A Random variable is a measurable map from a probability space to any measurable space
Let [ilmath](\Omega,\mathcal{A},\mathbb{P})[/ilmath] be a probability space and let [ilmath]\Epsilon:\Omega\rightarrow\mathbb{R} [/ilmath] be a random variable
(that means it is a measurable map FROM a probability space to a measurable space recall)
Then:
TODO: Finish this because it's iffy
