Re: Random points on a sphere- variance


"David L. Wilson" <dwilson314@xxxxxxxxxxxx> wrote in message
news:oKSdndB8vMWWw7DeRVn-iQ@xxxxxxxxxxxxxxx
>

>> unit area anywhere on the sphere is constant.
>
> If I understood correctly, he is after the *correlation* between azimuth
> and elevation (equivalently between latitude and longitude). Unless I am
> missing something, it is 0 but I have not had time to put together
> something that would constitute a proof.

I agree "variance of azimuth and elevation angles are related" could be
interpreted that way.
But if the pdf of azimuth is uniform and independent of elevation I think
theta and phi are statistically independent when defined in standard
spherical coordinates. Perhaps the OP could demonstrate this independence
from a simulation.


rusty





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