P: Choose the random variable before choosing a distribution
Common mistakes arise from modelling the wrong count or waiting time. Define what is counted, the observation window and any conditioning. A distribution name should follow those choices, rather than the appearance of a familiar keyword.
Worked example or practice scenario
In a toy homogeneous Poisson process with rate 2 per hour, N(3) has mean 6. The wait until the first event has exponential rate 2 and mean .5 hour. The wait until the third event has a different distribution and mean 1.5 hours.
Try this next
Write three different questions about the same process: a count in a fixed window, no event before a time, and the third arrival time. Check that each answer’s units match the variable. Do not use these assumptions for changing-rate processes without adjustment.
Reading sources
ActNet editorial guide · October 1, 2026 · Original illustrative examples.