Normal distribution pdf function returns value >1?

Question

I am using the function scipy.stats.norm.pdf() in the following way:

>>> scipy.stats.norm(scale=0.00026)
>>> scipy.stats.norm.pdf(0.0005)
241.48

Where scale is the standard deviation parameter. How is this possible? 241.48 is clearly not a probability.

Answer 1

You'e are evaluating the pdf not the cdf, and with small variance (i.e. scale) at the point $x=0.0005$ you will have the value $$\frac{1}{\sqrt{2\pi}\sigma}e^{-x^2/2\sigma^2}=\frac{1}{\sqrt{2\pi}\times 0.00026}e^{-0.0005^2/2\times 0.00026^2}=241.48$$