Understanding the Relationship Between Gaussian Math and Graph Width

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SUMMARY

The discussion centers on the mathematical relationship between Gaussian functions and the concept of graph width. Specifically, the Gaussian function is expressed as exp(-ax²), where the parameter 'a' is related to the width of the graph. The correct relationship is established as a = 1/(2σ²) when comparing it to a normal distribution. However, the term "width" requires clarification, as it is not universally defined and can vary based on the specific interval being analyzed.

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  • Familiarity with normal distribution concepts
  • Knowledge of parameters affecting graph shapes in mathematics
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For a gaussian of the form:

exp(-ax2)

How is a related to the width of the graph? I can see that if I compare with a normal distribution

a = 1/2σ2. Is that correct?
 
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What do you mean by "width" of the graph? Where are you measuring the "width"? Between x= -1 and x= 1 the width is e^{-a^2}. As for "a= 1/2\sigma^2", that makes no sense because there is no "\sigma" in the original function.
 

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