Pi in Normal Distribution Equation

[baron.cecil]

Does anyone know why the ratio of circumference to diameter is in the normal distribution equation? I know the normal distribution models most natural phenomena, but how the heck did Pi did up in there?

Thanks,
Dan

 

[Deleted member 4993]

The same reason why it comes up in Buffon's needle problem, or Drunkard's walk problem - for that matter area of a circle problem.

 

[royhaas]

In fact, the "complicated derivation" depends on the circumference of a unit circle being \(\displaystyle 2\pi\).