rm(list=ls())
library(plot3D)

#-----------------------------------------------------#
#---   Classical and Bayesian inference (AMS132)   ---#
#---   Class 8: maximum likelihood estimator      ---#
#-----------------------------------------------------#


#-- data:
data=c(3, 1.5, 2.1)

#-- some description od the data:
n=length(data) 

#-- likleihood function:
curve(x^n*exp(-x*sum(data)), 0, 10, ylab="likelihood function", xlab=expression(theta), lwd=3)

curve(n*log(x)-sum(data)*x, 0,10,  ylab="log likelihood function", xlab=expression(theta), ylim=c(-60,10), lwd=3)
abline(v=1/2.2, col="red", lwd=3)