Understanding the Relationship Between Gaussian Math and Graph Width

[aaaa202]

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?

 

[HallsofIvy]

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.