Consider the following data from 50 Bernoulli Trials
Let theta be the probability of the observing a one for any single trial.
a) Find the likelihood of any sequence of s trials containing y ones.
b) If the prior on theta is uniform such that p(theta)=1, find an expression for the posterior distribution for theta after 10 trials.
What is the maximum likelihood estimator of theta?
c) Find an expression of the posterior after another 30 trials. In what sense has the prior been updated?
