TITLE: Changing normal distribution given new data
QUESTION [1 upvotes]: Assume as in the  picture above, we have two points $A$ and $B$. Each has a location with a normal distribution of error, i.e. $A$ is believed to be at $x=0$ with an error of $σ=1$, and $B$ at $x=35$ with an error of $σ=1$.
Point $A$ now knows that it is only $33$ meters (exactly) away from point $B$.

How would this affect the normal distribution of error of point $A$?
What would also happen to the distribution if the $33$ meters has a margin of error?

REPLY [0 votes]: we can represent the joint probability distribution as in this picture above.
Having a relation d=x-y can be represented on the joint distribution by straight line with the more probable position presented as the projection of the center on the line.as represented here
The error of the distance can be represented by making the line thick.
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