Assume that X is discrete random variable with P(X=1) = theta and P(X=2)=1-theta. Three independent observations of X are made:
x1=1, x2=2, x3=2
a) Find out the method of moments estimate of Theta
b) What is the likelihood function?
c) What is the maximum likelihood estimate of theta?
d) if capital theta has a prior distribution that is uniform on [0,1] what is its posterior density?