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Today at school we discussed probability distributions and as usual my mind wandered off and I started thinking:

Normally when we have a die, you can make a binomial distribution. So I thought, if you have a die with, instead of 6 sides, an infinite amount of sides, wouldn't the binomial distribution become a normal distribution?

If yes, can you also say that when a normal distribution is 'simplified' (with simplified I mean for example going from an n-sided dice to a 6 sided die) it always turns into a binomial distribution, or is that just the case for some examples (like this die example, which is what I assume is true)?

  • p.s. This was our first lesson on probability, so what I might say might sound ridiculous. At the beginning of each chapter I always wonder off like this, sometimes I get nice results and sometimes I fail epicly.
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    It wouldn't become a normal distribution, but under certain conditions it would tend to a Poisson distribution. See [this](http://en.wikipedia.org/wiki/Poisson_limit_theorem).2012-12-19
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    There is, however, a normal distribution approximation to the binomial distribution: http://en.wikipedia.org/wiki/Binomial_distribution#Normal_approximation2012-12-19
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    In fact, Poisson, binomial, and negative binomial distributions are very closely related. And there is a certain intuition towards taking the limiting case of a discrete distribution and obtaining a continuous distribution. However, the PMF of a discrete distribution and the PDF of a continuous distribution are not quite equivalent; their evaluation at a given value does not mean the same thing.2012-12-19
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    Aren't a dice and a die the same?2012-12-19

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