6. Let (331,13, - -- ,mn) be i.i.d. samples a random variable X with the fol lowing probability density function: f()_ 1 if6 0 is unknown. In an experiment, the following observations / samples were obtained from the above distribution. 331 = 0.3,mg = 0.4, 333 = 02,314 = 1.0, $5 = 0.9 (a) Find the posterior distribution of 6 for the given data set based on the following prior distribution on 0: 7r(6) = 0.5_|6| (b) Show how you will simulate an observation from the posterior distri bution in (a) assuming you can only simulate U from a Uni f orm([0, 1]) distribution. Give the explicit function relating 6 to the simulated observation U