Probability and Statistics

Section 6.8 Bayesian Estimation

Let X be the binomial random variable with parameter m = 50 and 6 unknown. Suppose that the prior pdf WWW is the beta pdf with parameter oz = 100 and = 50. Suppose that we have performed n = 2 experiments with $1 = 10 and $2 = 35. (a) Show that the posterior pdf 713,03: is a constant multiple of the beta pdf with some parameter 04' and 6', and compute a," and '. (Hint: you do not need to compute K!) \f( c) Find the value of the Bayesian estimator 0 that minimizes the square of the error