# Why in PERT the activities duration follows a Beta distribution

studying the details of PERT/CPM, I'm perplexed when I read the formula of duration of an activity is

``````expected time = (opt. time + 4medium + pess. time) ÷ 6
``````

because it's following a Beta distribution.

I don't understand the cause. The Beta distribution is an extension, in continuous mathematics, of a Bernoulli distribution. This means that, in this distribution:

• every event is independent by the previous and the next;
• that are only 2 possible values, yes/no or similar;

I don't understand how to link these properties with the estimation of activities in a project.

Can you explain to me, please?

Thank

Estimation, like a lot of things in the PM world is both an art and a science. PERT is a good rule of thumb, but it is just a place to start.

For some projects I've seen estimates use (opt. time + medium + pess. time) ÷ 3 to show a larger possible variance.

But if it's a type of task that your team has done before (and maybe even has some data to show prior durations) you can more heavily weigh the medium as it is more likely that it will take that long again. (See Evidence Based Scheduling)

This is interesting. If you follow best practices for defining distinct activities to be estimated and tracked, then I think they really do meet these conditions.

• every event is independent by the previous and the next;

A well defined task or user story is independent in terms of the work required to do it. Of course, it may have dependencies in sequencing, but that's not the same thing as dependency in actually doing the work.

That is, given that Task A and Task B are started when "ready" (ie, when all their prerequisites are in place), then how long it takes to do one should have no bearing on how long it takes to do the other.

• there are only 2 possible values, yes/no or similar;

The task is Done or Not Done. Best practice is not to track %complete, because there's no value delivered until it's Done. (And you don't reaaally know how much work is left until the amount left is 0.)

Does that help?