Asked about The distributions you will actually meet
I hand you a quantity. How do you decide which distribution to model it with?
An answer that works
By what generated it rather than by looking at a histogram. One trial with two outcomes is Bernoulli, and a count of successes out of a fixed n is binomial. A count of events in a window with no natural maximum is Poisson. The time until the next event is exponential. A measurement built from many small independent contributions, or any average, is normal. A quantity that is a product of effects rather than a sum — latency, file size, income — is log-normal or heavier.
Then they push further
You model support tickets per hour as Poisson and the variance is four times the mean. What does that tell you?
That the arrivals are not independent. A Poisson has variance equal to its mean by construction, so anything above that is overdispersion: tickets arrive in bursts, usually because one incident generates many. A Poisson model will badly understate the worst hours, which are the ones staffing has to cover, and a negative binomial is the usual replacement.
Why is the exponential the odd one out?
It is memoryless: having waited three minutes leaves the distribution of the remaining wait exactly as it was at the start. That is a strong claim and it fails for most real queues, where a request that is already slow is stuck on something and will stay slow, so retry and timeout policies built on it tend to be wrong.
What gets marked up
Strong answers reason from the generating process. Naming distributions from the shape of a histogram is the weaker answer and gets probed.
Reading an answer is not being able to give one. The section that teaches this is The distributions you will actually meet, 4 hours of Probability & statistics.
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