% filename: inference_example_1.m

% This script plots the likelihood function for Example 1 in the Introduction to Inference presentation.  In the example, WRW were the colors of three marbles drawn from a large bag, and the goal was to give plausible values for pi, the proportion of reds in the bag.

% **********

% create a vector of candidate values of the parameter pi, and compute the likelihood L at each of those values.  Note that .^ and .* are element-by-element exponentiation and multiplication respectively.

p = [0:0.01:1];
L = p.*((1-p).^2);

% plot the likelihood function against pi:

plot(p,L)
xlabel('\pi')
ylabel('Likelihood L(\pi )')