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.

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Layla Love · Accepted Answer

If you have equal normal errors in   x and   y, you get a Rayleigh distribution. The probability distribution function in r is   f  (  r  ,  σ  )  =      r          σ      2        exp  ⁡  (            −              x        2                    σ      2        ). Because of the factor r it is analytically integrable.

Consider a position measurement that is prone to a random error in any direction. This would mean th

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