# Talk:Multivariate random variable

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Field: Probability and statistics

## Probability space

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)