#   binomial for US presidential data
#  Edps 587
#  C.J.Anderson
#
# Taller who won for elections 1932 - 2008
#
#  See http://en.wikipedia.org/wiki/Heights_of_United_States_Presidents_and_presidential_candidates
#  Read in data
#  Plots histogram
#  Overlay Poisson distribution
#
#
# Plot of
#  Taller who won for elections 1932 - 2008
#  See http://en.wikipedia.org/wiki/Heights_of_United_States_Presidents_and_presidential_candidates

# Possible values for probability
pi <- seq(0,1,.01)

# Observations
N <- 19
y <- 15
p <- y/N

num <-length(pi)

bincoeff <- factorial(N)/(factorial(y)*factorial(N-y))
 
binprob <- bincoeff * pi**y * (1-pi)**(N-y)

plot(pi,binprob, type='l',
     main="Likelihood Function for Binomial",
     sub="Note that y=15, N=19, p=.79",
     xlab=expression(paste("Possible values of the probability ", pi)),
     ylab="Value of the Likelihood Function"
)

lnL <- seq(0,max(binprob),.001)
prop <- rep(p,length(lnL))
lines(prop,lnL)