by Ben Watson
Last Updated October 18, 2019 09:20 AM

As part of one of my Random Signal Theory assignments I came across the sample space of random variables X and Y represented by the set:

$S_{X,Y} = \{(x_i,y_j):(i,j),i,j=1,2\}$

How would I interpret this? What I think it means is: "Sample space $S_{X,Y}$ contains $x_i$ and $y_j$ such that $i$ and $j$ can take the values $1$ or $2$"

Which would result in the sample space containing 4 variables: $x_1,x_2,y_1,y_2$

However I am mostly going on intuition and lack a true understanding of how exactly to construct and interpret this sort of notation.

Another option in my mind is that it is somehow specifies that: $x_1=1, x_2=2, y_1=1, y_2=2$ Which would fit the context of the problem, but again I have no idea how to derive this meaning from the above statement.

Can someone please explain exactly what this does mean and/or point me in the direction of learning resources that would teach me the basics of understanding this set notation?

I would interpret this as the set of pairs $(x_i, y_j)$ with $i,j = 1, 2$. Explicitly, the set $$ S_{X,Y} = \{(x_1, y_1), (x_2, y_1), (x_1, y_2), (x_2, y_2)\}. $$

Updated July 07, 2018 13:20 PM

Updated September 28, 2018 15:20 PM

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