Intersection of two gaussian distribution functions

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Discussion Overview

The discussion centers on finding the intersection points of two Gaussian distribution functions, particularly when the variances are different. Participants explore the mathematical formulation and implications of this intersection.

Discussion Character

  • Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant requests formulas for the intersection of two Gaussian functions, specifying the need for different variances.
  • Another participant questions the use of the term "intersection," suggesting it is more commonly associated with sets rather than functions.
  • A third participant clarifies that "intersection" refers to the points where the two curves share the same (x, y) coordinates on a graph.
  • One participant proposes that the intersection can be found by setting the two Gaussian expressions equal to each other and solving for x.
  • There is mention of a messy calculation that would benefit from using "tex" tags for clarity.

Areas of Agreement / Disagreement

Participants express differing interpretations of the term "intersection," with no consensus on its definition in the context of functions versus sets. The discussion remains unresolved regarding the best approach to find the intersection points.

Contextual Notes

There are indications of missing assumptions regarding the conditions under which the intersection is calculated, and the discussion does not resolve the complexity of the formulas involved.

hkBattousai
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Can you please give me formulas which give intersection of two gaussian function

f(x, mu, sigma) = 1/sqrt(2*pi*sigma^2) * exp(-(x-mu)^2 / (2*sigma^2))

for the case variances are different.


(Note: I think it is time I learn how to use "tex" tags, do you know a good tutorial?)
 
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What do you mean by "intersection"? The term intersection is usually used when talking about sets, not functions.
 
mathman said:
What do you mean by "intersection"?

The two points, where these two curves have the same (x, y) pairs on the graph.

Well, actually, I calculated the formula, but it is too messy without using "tex" tags...
 
Why not just set the two Gaussian expressions equal to each other, and solve for x?

Info on [noparse][/noparse] tag usage at Physics Forums can be found https://www.physicsforums.com/showthread.php?t=386951"
 
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