# Meaning of this Integral?

1. Mar 8, 2009

### jam_27

What is the statistical meaning of the following integral

$$\int^{a}_{o} g(\vartheta) d(\vartheta)$$ = $$\int^{\infty}_{a} g(\vartheta) d(\vartheta)$$

where $$g(\vartheta)$$ is a Gaussian in $$\vartheta$$ describing the transition frequency fluctuation in a gaseous system (assume two-level and inhomogeneous) .

$$\vartheta = \omega_{0} -\omega$$, where $$\omega_{0}$$ is the peak frequency and $$\omega$$ the running frequency.

I can see that the integral finds a point $$\vartheta = a$$ for which the area under the curve (the Gaussian) between 0 to a and a to $$\infty$$ are equal.

But is there a statistical or physical meaning to this integral? Does it find something like the most-probable value $$\vartheta = a$$? But the most probable value should be $$\vartheta = 0$$ in my understanding! So what does the point $$\vartheta = a$$ tell us?

I will be grateful if somebody can explain this and/or direct me to a reference.

Cheers

Jamy

2. Mar 8, 2009

### bpet

median positive value?

3. Mar 8, 2009

### tiny-tim

Last edited by a moderator: Apr 24, 2017