Rectangular range space

Oct 2009
21
0
Hello,

In one of my classes the lecturer referred to "the range space being (or not being) rectangular" as a justification of independence (or not) of two variables.

I don't understand what this use of 'rectangular' means specifically. Could someone give me a quick explanation. A Google search doesn't seem to turn anything up.

From the context it seems to mean that the variables have some sort of orthogonality (and that seems to be an intuitive definition of 'rectangular'), that is that they are not dependent on each other. But, in my head I feel like I'm just begging the question rather than understanding the concept on it's own.

How would you prove that a range space is rectangular? Do you just show that the value of one is not dependent on the other? But, again, it seems to me like I'm saying, 'They're independent because they're not dependent', and that's not very satisfying.

Thanks!
 

mr fantastic

MHF Hall of Fame
Dec 2007
16,948
6,768
Zeitgeist
Hello,

In one of my classes the lecturer referred to "the range space being (or not being) rectangular" as a justification of independence (or not) of two variables.

I don't understand what this use of 'rectangular' means specifically. Could someone give me a quick explanation. A Google search doesn't seem to turn anything up.

From the context it seems to mean that the variables have some sort of orthogonality (and that seems to be an intuitive definition of 'rectangular'), that is that they are not dependent on each other. But, in my head I feel like I'm just begging the question rather than understanding the concept on it's own.

How would you prove that a range space is rectangular? Do you just show that the value of one is not dependent on the other? But, again, it seems to me like I'm saying, 'They're independent because they're not dependent', and that's not very satisfying.

Thanks!
Range space is rectangular: The support is a < x < b and c < y < d.
 
Oct 2009
21
0
Range space is rectangular: The support is a < x < b and c < y < d.

Thank you for responding.

However, I'm sorry but I don't understand. Is there a definition of what 'rectangular' means in this context. (Maybe that's the support you're talking about, but I don't yet get it.)

I think I may have left something out of the original post, he was speaking about a joint range space of two variables.

Thanks again!
 

mr fantastic

MHF Hall of Fame
Dec 2007
16,948
6,768
Zeitgeist
Thank you for responding.

However, I'm sorry but I don't understand. Is there a definition of what 'rectangular' means in this context. (Maybe that's the support you're talking about, but I don't yet get it.)

I think I may have left something out of the original post, he was speaking about a joint range space of two variables.

Thanks again!
What I have posted is this 'joint range space' you're talking about. It defines a rectangular region. I suggest you discuss things with your instructor or go to a textbook or classnotes.