The probabilities for the 5 Regions are: After renaming the assignment variables in time to ones of relative position in space, this result can be immediately generalized to the three dimensional case; calculating the probability that two points lie within some geometry of each other. Example 3, Three dimensions, two “points” with Gaussian probability density functions. Assume person 1 is at the origin with an ellipsoidal Gaussian probability distribution: and person 2 is at point with probability:
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