(a) Assume a binomial distribution with parameter p: We want to estimate the parameter p which is...
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(a) Assume a binomial distribution with parameter p:
We want to estimate the parameter p which is P(outcome 1). Assume you have a training set of n data points of which n 1 are outcome 1 and n 2 are outcome 2. Derive the maximum likelihood estimator for p given these data.
(b) Recall that the beta distribution is the conjugate prior for the binomial.
Show that if the prior probability of p follows a beta with parameters (u.[) and the likelihood of p given the data set from (a) follows a binomial, the posterior probability of p given the data set is a beta distribution with parameters (N 1 + ?, N2 + (?)
(c) Given a posterior distribution of p that follows beta(?, (?), derive the expected value of p.
Related Book For
Statistics for Business and Economics
ISBN: 978-0132930192
8th edition
Authors: Paul Newbold, William Carlson, Betty Thorne
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