NavList:

In his post on 12-10-2010 at 13:24 Tom Sult quotes Frank's explanation of integrating the probability density over different areas. There Frank makes the familiar statement that the probability of a fix being inside the hat must be 25%. As we have be discussing, and arguing (I think proving) on the "Darned Hat" thread, this is simply not true.

Attached are two examples of contour plots of fix probabilities per unit area P(x,y). One shows a case where the probability that the fix is inside the hat is less than 15%. The other shows a case where it's greater than 66%. These results are a numerical integration of P(x,y) inside the contour sited at the top of the plot. (Since these contours are appropriately over, or under, estimates of the hat area, the actual percentages are even more compelling than quoted here.)

Moreover, just thinking about a hat area shrinking to zero, while P(x,y) remains less than 1.00, shows that the 75% rule is false.

JK
----------------------------------------------------------------
NavList message boards and member settings: www.fer3.com/NavList
Members may optionally receive posts by email.
To cancel email delivery, send a message to NoMail[at]fer3.com
----------------------------------------------------------------