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08:39
@masfenix The question may be quick but that kind of query is really much better posted on the main site.
 
4 hours later…
12:43
@masfenix, please ask that on the main site. There we have better facilities for asking & answering questions (e.g. formatting options will work) and the information
will be available for people with the same question. That isn't a chat item.
 
2 hours later…
14:32
@gung, @masfenix. Better: please search this site before posting a question.
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I will illustrate. Your question has two obvious keywords, so I first tried a search for questions with some upvotes that mention them both: stats.stackexchange.com/…. This had hundreds of hits and the top hit titles had little obvious relevance.
To refine the search, I noticed many hits referred to the negative binomial distribution. I therefore looked for posts that did not include the word "negative." A little risky, perhaps, because that's such a common word, but the objective is merely to find some relevant posts, not all of them.
Even that produced hundreds of hits. After a little reflection, it occurred to me that one key aspect of your question concerns the Poisson rate and focuses on the distribution (rather than estimation, etc.), so I looked for questions that mention both these terms: stats.stackexchange.com/…
This yielded just 20 results and the third one in the list has the title Q: Distribution of successes of poisson process followed by a binomial distribution. Le voila -- there's the duplicate.
Total time spent searching and thinking was under one minute. This is a typical experience and, typically, in my experience a minute of such iterated searching yields an answer in the majority of cases.
Perhaps that's because, through familiarity with this site, I have a good sense of which questions ought to have duplicates.
As a general rule, though, even someone new to this site (and even to statistics) ought to suppose by default that any question concerning basic concepts that can be clearly and simply stated likely has been addressed before.
3
That an answer is likely to exist already is, after all, what having over 100K+ questions answered during 10+ years means.
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