# Modelling uncertainty with probability distributions

Suppose we’re building a system with certain qualities that we’re interested in, e.g. response time, battery usage, etc. Each of the system’s qualities depends on our decision about components we use to build the system. We only know how the decisions impact the qualities of our system with uncertainty, e.g. deciding to use a GPS module will most likely add an extra 10µJ to our battery usage, but could add anything between 9-14µJ. Is it common to model this uncertainty using probability distributions? Is beta distribution a good choice here? Or would triangular or uniform distribution be more sensible in this case? In case of beta distribution, how do I work out the α and β parameters knowing the most likely and limiting estimates only?

Note: my knowledge in statistics is rather limited.

The beta, triangle and uniform distributions (the last a special case of the first) are all best used only when there are absolute limits on what is possible, e.g. all values must be within (0,1). It sounds as if 9 and 14 $\mu$J are likely or plausible limits only. You'd be better off using a distribution with infinite limits, such as a Gaussian, surprising though that may seem.