The birthday problem is a classic problem in probability.
Given \(n\) people in a room what is the probability that at least two of them have the same birthday ?
- Compute \(\mathbf{P}(n)\) assuming that a person being born on any day is equal.
In blogs Andy Gelman and Chris Mulligan talk about how the uniformity assumption may be incorrect and the effect this has on the birthday problem.
- Chris examined the uniformity assumption by looking at CDC data for one year in terms of number of births. He provides R code (that I slightly adapted) that you can run in RStudio to plot the number of births through the year. How different is this from uniform ?
- Given this observed distribution he then computes the difference between the result of the birthday problem given the observed distribution versus a uniform distribution. This is done using Monte Carlo simulation in R (again slightly adapted by me). Does the deviation from the uniform distribution have a strong effect ?
