TITLE: probability calculation for position measurement being inside a circle
QUESTION [0 upvotes]: Consider a position measurement that is prone to a random error in any direction. This would mean that the position would be in a circle where the probability curve taken across the diameter would show a normal distribution. 
How can the probability be calculated that the position measurement is inside another circle?
I can ignore the cases where the circle of probability is entirely inside the detection circle (because the probability of being in the detection circle has reached 100%) and when it is entirely outside the detection circle (probability falls to 0%), i.e. the cases where the two circles do not intersect.

REPLY [0 votes]: If you have equal normal errors in $x$ and $y$, you get a Rayleigh distribution.  The probability distribution function in $r$ is $f(r,\sigma)=\frac r{\sigma^2}\exp(\frac {-x^2}{\sigma^2})$  Because of the factor $r$ it is analytically integrable.
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