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    Re: A simple three-body fix puzzle
    From: Tom Sult
    Date: 2010 Dec 10, 21:08 -0600

    Glad to hear it but I must say I am still confused by the assertion
    that the probability of being at the center of a perfect crossing 3
    body fix is "0"
    Thomas A. Sult, MD
    3rd Opinion
    1415 First First St. South #5
    Willmar, MN 56201
    320 235 2101 Office
    www.3rdOpinion.us
    tsult@mac.com
    
    
    
    
    
    
    On Dec 10, 2010, at 4:27 PM, Frank Reed wrote:
    
    > Tom, you wrote:
    > "It seems to me the point of this is that the best probability of
    > location is a "donut" that roughly follows the lop's around the hat.
    > We have learned that we have perhaps a 25% +/- the details chance of
    > being close to any "center" of the hat. And we can calculate the
    > probability distribution of our location along any one of our LOP's.
    > If the gausien distribution is centered on the LOP then we have a
    > "fuzzy donut" probability and not a Position. "
    >
    > No, no donuts. This is one of the things that can go wrong when
    > people have this discussion. The point with highest probability is
    > at the fix, inside the triangle formed by the crossing LOPs. The
    > ellipse of non-negligible probability, however, extends well outside
    > the triangle. Picture a low, broad "hill" of probability with a
    > "bell curve" cross-section. There is a 75% chance of being outside
    > the triangle. But this doesn't mean that there is a "hole" in the
    > donut. The location of maximum probability is right where we have
    > been discussing: at the "symmedian" point. But the triangle is NOT
    > an approximation to the error. The probability steadily decreases as
    > you move away from the fix, and this applies to any number of lines
    > of position (greater than one). EVERY fix yields an error ellipse
    > (or better yet, a family of concentric error ellipses, each
    > reprsenting a lower probability than the one before it). That's the
    > final product. The center of that error ellipse, which is the high
    > point on a low, flat hill, is located at that point inside the
    > triangle, but the sides of the hill decline away much more gradually
    > than most people expect.
    >
    > -FER
    >
    >
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