# epage 74
#
# Written by:
# -- 
# John L. Weatherwax                2009-04-21
# 
# email: wax@alum.mit.edu
# 
# Please send comments and especially bug reports to the
# above email address.
# 
#-----

Nsim = 10^4

# small/large values for lambda (the value of 1/mean)
#
lambda = 2

X = NULL
for( ii in 1:Nsim ){
  k = 0
  v = rexp(1,rate=lambda)
  while( v < 1 ){
    v = v + rexp(1,rate=lambda)
    k = k+1
  }
  X[ii]=k  
}

xRng = seq(min(X),max(X),1)
brks = c( xRng[1] - 0.5, xRng + 0.5 )
hist(X,freq=F,breaks=brks,main="Poisson from Exponential")
lines( xRng, dpois(xRng,lambda), col="Blue" )