#=====================================================
# Simulation of the probability distribution of batting
# average.
#=====================================================

#-----------------------------------------------------
# 1.  Simulate n trials m times, with prob p of success
# on each trial.  Store counts of successes in hits.
# Calculate proportion of successes and store in batave.
#-----------------------------------------------------

m=100
n=30
p=.26
hits=rbinom(m,n,p)
batave=hits/n

#-----------------------------------------------------
# 2.  Plot histogram of hits.
#-----------------------------------------------------
bounds=seq(-.5,n+.5,1)
hist(hits,breaks=bounds,freq=FALSE,xlab="batting average",
  ylab="density",main="Distribution of Hits")

#-----------------------------------------------------
# 3.  Plot histogram of batave.
#-----------------------------------------------------
windows()
bounds=bounds/30
hist(batave,breaks=bounds,freq=FALSE,xlab="batting average",
  ylab="density",main="Distribution of Batting Average")