#
# 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.
# 
#-----

# Exercise 29:
#
waiting_game = function( nDraws=100, targetNumFlips=3 ){
    nFlipsNeeded = matrix( 0., nrow=nDraws )
    for( ii in 1:nDraws ){
    # Flip a coin until we get a total of targetNumFlips ones:
    # 
    totalFlips = 0 
    nOnes = 0
    while( nOnes < targetNumFlips ){
      flip = rbinom( 1, size=1, prob=0.5 )
      totalFlips = totalFlips + 1
      if( flip==1 ){
        nOnes = nOnes +1
      }
    }
    nFlipsNeeded[ii] = totalFlips
  }
  nFlipsNeeded
}

# Determining the max/min size of the bins seems to be rather tricky.
# Thus we will just hard code the bin size
#
min_value = 3
max_value = 25 
bins = seq( from=(min_value - 0.5), to=(max_value + 0.5), by=1.0 )

nDraws = c(5000,1000,500,100)

M = matrix( 0, nrow=length(bins)-1, ncol=length(nDraws) )
for( ii in 1:length(nDraws) ){
  wg = waiting_game(nDraws[ii])
  M[,ii] = hist( wg, breaks=bins, plot=F )$intensities
}

#postscript("../../WriteUp/Graphics/Chapter2/prob_29_hist.eps", onefile=FALSE, horizontal=FALSE)

barplot( t(M), beside=T, main="MC distribution", ylab="frequency", xlab="5000,1000,500,100 number of experiments" )

#dev.off()

# whats the expected number of rolls needed to get three looks like it is ~ 4
#
t(M) %*% matrix( 1:(length(bins)-1), nrow=(length(bins)-1), ncol=1 )