I am interested in calculating the uncertainty due to counting statistics such that I can obtain vertical error bars for a histogram.
I have a probability density function that tells me the probability of a count at $t>0$. The pdf is not normal; it is the sum of two decaying exponentials. The domain of the pdf is $0$ to $\infty$; however, the data is binned between $0$ and some $t_\text{max}$. How do I use the pdf to calculate the standard deviation in the number of counts for each bin?