# Binomical vs poisson distribution in Simulations

1. Sep 14, 2006

### hagen

Hey, I want to write a Computer Simulation in C++, which simulates the development of a DNA sequence with a probability to mutate x in one "generation". I do have a variable number (=n) of copies of this DNA. Now one might think, to simulate the mutation by simply:
sum(n*Poisson distributed random variable(x) ) ​
to get the number of mutated DNA copies. But this would be too slow.
So my question is, could I also just create a
binomically distributed random variable and multiply it by n * x​
to get the number of mutated DNA's? Or is this statistically incorrect?
If not, how might I set the Params for the Bin. dis.? Can I take 1 as a mean and multiply the result x or has the mean to be x? And how do I set / transform the variance of the distribution in a ratio to number of copies.
As you might probably have guessed, I'm a beginner in statistics, but i would be really grateful for any help. Thanks in advance,
Hagen

2. Sep 15, 2006

### radou

Hm, if I remember correct, there is a link between the binomial and Poisson distribution.. Poisson's probability function is given with $$f(x)=\frac{\lambda^x}{x!}e^{-\lambda}$$. Now, I think you can put $$\lambda=mp$$, where the number of repetitions of a Bernoulli scheme experiment $$m \rightarrow \infty$$ and it's probability $$p \rightarrow 0$$.

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