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Re: Probabilities & Estimations -- A Review
From: John Karl
Date: 2013 Apr 6, 12:59 -0700

Gary,

Yes, the probability that the true location is less than 1-sigma from the intersection of the two LOPs is indeed 39.4%. We can see this from a simple calculation of the circular probability distribution.

And thanks for pointing that out, because it's a check on my numerical calculations, as shown in the first attachment. But this result is only for right-angle crossings of the two LOPs. For other angles it grows less as the intersection angle decreases. The 2nd and 3rd attached figures show the 1-sigma number decreasing to 28% for 45-deg intersections, and down to 16% for 20-deg intersections.

I should have been more clear on that point.

The sigmas of 20 units can be scaled off the axes in the figures. (I found it too much trouble to plot the 1-sigma circle around the intersections -- computers!)

Thanks for the comment,
JK
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