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    Re: Position lines, crossing.
    From: Lu Abel
    Date: 2006 Dec 09, 12:45 -0800

    George Huxtable wrote:
    > In fact, if any systematic errors have been properly corrected for,
    > and only random scatter remains, the simple truth is this. Only on one
    > time in 4 will the vessel be inside that triangle at all, and 3 times
    > in 4 it will be somewhere outside it, though in the vicinity. This is
    > a simple statistical truth, easily proved, but one that mariners are
    > most reluctant to accept, because it is so contrary to what they have
    > been taught.
    First of all, thanks for such an insightful post.  Like most, I've been
    taught that a cocked-hat fix is a wonderful thing to have; that one must
    surely be inside the cocked hat.  Even though I know enough of
    statistics, I never thought of the statistics of a cocked-hat fix.
    But now a question:  Is the probability that I'm inside the cocked hat
    1 in 4 or 1 in 8??
    I presume your "simple statistical truth" is that, absent any additional
    information about the quality of the LOPs, there is a 50% chance that my
    true position is on one side or the other of the LOP.
    To be inside the cocked hat, it seems to me that I have to be on one
    particular side of each of the LOPs, which makes for a probability of
    1/2^3 or 1/8.
    What am I missing?
    Lu Abel
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