simulate poisson distribution traffic I am given a mean and variance for the number of occurrences over 80 days, and I am generating simulation traffic for each of the 80 days. For a given mean, its easy to plug it into the poisson distribution equation and get the simulated daily output. All you have to do is divide the 80 day mean by 80 to get the daily mean. But how do you incorporate the variance into the simulation?  
 A: For a Poisson distribution the mean and variance are the same. If you are given one, you have the other as well. Note, the standard deviation is the square root of the variance. This is useful for mental arithmetic. For $n>40$ or so, the Poisson distribution is a good approximation of the normal distribution. Suppose that 100 people answer yes to a question. We want to know what approximate 95% confidence intervals are and that would be Answer +/- 2 SD. Since 100 is 10 squared and 10 is the SD, thus 100-2*10 to 100+2*10 or 80 to 120 would be the confidence intervals, or if you wish, the survey answer is +/- 20% 19 times out of 20.
Note, however, that what is usually reported is incorrect, that is, if there are 400 questions and only 100 yes answers, the answer accuracy usually reported is +/-2*20/400 or +/- 10%. However, that is willful misrepresentation as 400 questions does not relate to uncertainty of yes answers which would be +/- 20%. Thus, the polling agencies misrepresent the goodness of their work by lying to us.
