# This program calculate the theoretical probabilites for the 
# classical birthday problem.
# In addition, we simulate the outcome of birthdays and identify
# the dates which at least two persons were given birth in a group
# of n.
# Created 040315 by C. Andy Tsao.

library(MASS,survival)

psbd<-function(x,n)
{a<-x-1; b<-x-n+1;v<-1-prod(b:a)/x^(n-1);return(v)}

x<-365; daylist<-seq(1:x)
n<-73;
psbd(x,n);
ssample<-sort(sample(daylist,n,replace = TRUE));
ssample;
duptf<-duplicated(ssample)
dupdates<-ssample[duptf==TRUE]
as.date(dupdates)