log.likelihood <- function( y, mu, sigma ) {

  s <- 0

  n <- length( y )

  for ( i in 1:n ) {

    s <- s + abs( y[ i ] - mu ) / sigma

  }

  ll <- - s

  return( ll )

}

likelihood <- function( y, mu, sigma ) {

  return( exp( log.likelihood( y, mu, sigma ) ) )

}

mu.grid <- seq( 0, 10, length = 500 )

sigma <- 4

y <- c( 1, 2, 9 )

plot( mu.grid, likelihood( y, mu.grid, sigma ), type = 'l',
  lwd = 2, xlab = 'mu', ylab = 'Likelihood' )

plot( mu.grid, log.likelihood( y, mu.grid, sigma ), type = 'l',
  lwd = 2, xlab = 'mu', ylab = 'Log Likelihood' )

y <- c( 1, 2, 5, 9 )

plot( mu.grid, likelihood( y, mu.grid, sigma ), type = 'l',
  lwd = 2, xlab = 'mu', ylab = 'Likelihood' )

plot( mu.grid, log.likelihood( y, mu.grid, sigma ), type = 'l',
  lwd = 2, xlab = 'mu', ylab = 'Log Likelihood' )