Talk:Multivariate random variable

From Wikipedia, the free encyclopedia
Jump to: navigation, search
WikiProject Statistics (Rated Start-class, Low-importance)
WikiProject icon

This article is within the scope of the WikiProject Statistics, a collaborative effort to improve the coverage of statistics on Wikipedia. If you would like to participate, please visit the project page or join the discussion.

Start-Class article Start  This article has been rated as Start-Class on the quality scale.
 Low  This article has been rated as Low-importance on the importance scale.
 
WikiProject Mathematics (Rated Start-class, Low-importance)
WikiProject Mathematics
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
Start Class
Low Importance
 Field: Probability and statistics

Probability space[edit]

Quote:

More formally, a multivariate random variable is a column vector X = (X1, ..., Xn)T (or its transpose, which is a row vector) whose components are scalar-valued random variables on the same probability space (Ω, \scriptstyle \mathcal{F}, P), where Ω is the sample space, \scriptstyle \mathcal{F} is the sigma-algebra (the collection of all events), and P is the probability measure (a function returning every event's probability).

The probability space of the scalar components of this vector is the same as the probability space of the entire vector? The sample space \Omega for individual components should correspond to the cardinality of that specific scalar random variable, or perhaps I don't understand what "same" means here. 217.77.157.57 (talk) 11:02, 19 February 2013 (UTC)