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My professor just gave us the question as I wrote it above, and we seriously didn't get it , I mean what should we answer him with ? , did he ment the basic differences ? If he did , then why it mentioned "THE MAIN" he could have wrote only the "differences" ?? I hope I'll find the answer for this question. PS : if you wandering why we didn't ask the professor these questions directly? Will, my answer is : "We actually did asked him the same questions but he kept silence and never answered them "

itsmeDio
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  • I would guess continuous vs. discrete domains. – David P May 18 '21 at 04:32
  • @TeresaLisbon Without having attended the lectures, I don't think we can fairly blame the professor for a lack of context. – Théophile May 18 '21 at 04:39
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    @Théophile Good point. I think that's a lack of respect (there was a meta thread about this, so it's double irony that I do this having seen the thread). I'm sorry, I'll delete and rephrase : This question contains useful information – Sarvesh Ravichandran Iyer May 18 '21 at 04:40
  • A Poisson random variable counts the number of times a particular event takes places on a certain interval of time of a certain region of space. Events must occur independently, two events cannot occur simultaneously, and the average number of events that occur on an each interval of time or each region of space is approximately constant. On the other hand, a binomial random variable counts the number of successes among a fixed number of trials. Only two outcomes per trial are allowed, the the probability of success must be the same on each trial, and the trials must be independent. – Matthew H. May 18 '21 at 04:52
  • we don't blame anyone , i wrote the question because i know someone will commenting about asking the prof. Thank you – itsmeDio May 18 '21 at 04:56

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They are completely different. If a Poisson random variable has mean $5$ and a binomial random variable has parameters $25, 1/3$, then the two models are not even close. However, there is a key similarity between poisson and binomial random variables that is when $\lambda=np$, with $n$ large and $p$ small, then the poisson and binomial distributions are can approximate one another. In this case, and in this case only, the main difference is that the poisson can take any non negative integer value (albeit with very small probability), while a binomial random variable can take only the integer values between $0$ and $n$.

Vons
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