# Automatic selection of plot bounds for Normal pdfs in a combined chart

Suppose an app's user specifies several Normal priors by setting the mean and variance for each. I'd like to display a combined plot with the prior pdfs, like that on the figure. .

Q: What is a good way to compute the plot bounds for reasonable visualisation?

I've considered alternatives, eg:

• set the smallest $$(\mu_i - 3\sigma_i)$$ and largest $$(\mu_i - 3\sigma_ i)$$ for the left and right bound, respectively. (Here, $$i$$ indexes the priors.)
• set the bounds using a small threshold for the derivative of each $$pdf_i$$.

The difficulty is caused by possibly disparate priors: flat vs sharp. There are UI solutions (e.g. user-defined plot bounds) but they're laborious, and ignore the initial bounds choice for display initialisation.