bernoulli.likelihood <- function( theta, n, s ) {

  return( exp( s * log( theta ) + ( n - s ) * log( 1 - theta ) ) )

}

theta.grid <- seq( 0, 1, length = 500 )

n <- 400

s <- 72

plot( theta.grid, bernoulli.likelihood( theta.grid, n, s ),
  type = 'l', xlab = 'theta', ylab = 'Likelihood Function' )

plot( theta.grid, bernoulli.likelihood( theta.grid, 4000, 720 ),
  type = 'l', xlab = 'theta', ylab = 'Likelihood Function' )

# figure on page 18, part 3 of the lecture notes

pdf( "chapter-2-page-18-figure.pdf" )

par( mfrow = c( 1, 2 ) )

plot( theta.grid, bernoulli.likelihood( theta.grid, n, s ),
  type = 'l', xlab = 'theta', ylab = 'Likelihood Function' )

narrow.theta.grid <- seq( 0.12, 0.24, length = 500 )

plot( narrow.theta.grid, bernoulli.likelihood( narrow.theta.grid, 
  n, s ), type = 'l', xlab = 'theta', ylab = 'Likelihood Function' )

dev.off( )

# figure on page 19, part 3 of the lecture notes

bernoulli.log.likelihood <- function( theta, n, s ) {

  return( s * log( theta ) + ( n - s ) * log( 1 - theta ) )

}

pdf( "part2-page-19-figure.pdf" )

par( mfrow = c( 1, 1 ) )

plot( narrow.theta.grid, bernoulli.log.likelihood( narrow.theta.grid, 
  n, s ), type = 'l', xlab = 'theta', ylab = 'Log Likelihood Function' )

dev.off( )