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So I have in excel the numbers of 0 to 36. Following the poisson distribution [POISSON.DIST(0,18,,FALSE)], i found the probability of each number to come out. The computer generates a random number between 0 and 1 and then it looks up that number in the range of intervals and tells me what number was for example 4, 18, 35 or any number between 0 and 36. Is there a way to find the minimum amount of times a random number is generated in order that all numbers have come out at least once?

Salvatore Garza
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Given a truly random process, there is no minimum. You can make the probability of generating all numbers as close to $1$ as you like by generating enough numbers, but you cannot make it equal $1$.

For Excel, the minimum number of tries before you generate every number is a function of exactly what pseudorandom process it uses to generate the "random" values between $0$ and $1$. But that's a number-theory question, not probability, and it requires explicit knowledge of the algorithm used by Excel.

Also, a true Poisson distribution has no upper bound on the possible outcomes. It should be possible that it will sometimes generate a number greater than $36$.

David K
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  • Look: https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-xpf1/v/t34.0-12/11040320_10206622450903985_176828067_n.jpg?oh=52f9017d49997fa9b7d8b77a63898f4e&oe=54FEE763&gda=1425998615_e9418499763ee04825f135236082714a The probability of having a number greater than 36 is of 5.7519E-05. When I make the graph it looks like a Gaussian distribution. Poisson and Gauss are totally different right? – Salvatore Garza Mar 09 '15 at 04:36
  • Poisson (with sufficiently large mean) and Gaussian both have a peak with tails on both sides, but the Poisson's left tail ends at zero. You are doing a truncated Poisson, which may be perfectly OK depending on how you use it. In practice with Excel it will be truncated anyway since there are only finitely many values the random generator can produce. – David K Mar 09 '15 at 05:24