On 28 Mar 2000 07:15:35 -0800, [EMAIL PROTECTED] (dennis roberts) wrote:
> here is a contest question: best answer wins something ... what? i have no idea
>
> what would be a good VERBAL description of the bivariate normal
> distribution ... as the population rho between X and Y goes from 0 to 1?
> (and, in this description, indicate in particular what it would look like
> if rho = 0 AND if rho = 1
I can visuallize it and describe it better with 3 dimensions. In
three dimensions, it looks like a fuzzy flying saucer-style of UFO.
It is oval or elliptical in a cross-sectional view, which is pretty
much how I imagine the UFO. But, *fuzzy* -- hard edges don't really
exist, so if you look harder or if there is a brighter light, then the
ellipse is smaller. (And, maybe, there are some sort of "racing
stripes" superimposed on the image, at the distance of 1-SD out from
the center, and 2-SD out, where it really is becoming transparent, and
3-SD out, a thin demarking that seems like the hint of a force field.)
If rho = 0, then you see the saucer straight-on as the sphere or, in
2-D, a circle, but one which is firmer or brighter in the middle. If
rho approaches 1.0, then you see it edge-on, as just a single straight
line, which similarly fades out, at the extremes.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
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