# Math Help - Mean of a probability density function

1. ## Mean of a probability density function

I have a probability density function (PDF), $\vartheta(r)$, where $r\in[0,\infty]$. So the mean of the PDF ( $\bar{r}$) is calculated by $\int_0^\infty r\vartheta(r)dr$.

One can say that $\lim_{t\to\infty}\frac{\int_0^t r\vartheta(r)dr}{\int_0^t \vartheta(r)dr}=\bar{r}$.

But is it correct to state that $\frac{\int_0^t r\vartheta(r)dr}{\int_0^t \vartheta(r)dr}\approx\bar{r}$ when $t\gg\bar r$ ?