Question below:

Let (m1,x2,~- ,mn) be i.i.d. samples a random variable X with the fol- lowing probability density function: ()_ 1 ua 0 is unknown. In an experiment, the following observations / samples were obtained from the above distribution. 11:1 = 0.3,232 = 0.4,:33 = 0.2,:84 = 1.0,:35 = 0.9 (a) Find the posterior distribution of 3 for the given data set based on the following prior distribution on 6: 7116) = Obs'9' (b) Show how you will simulate an observation from the posterior distri- bution in (a) assuming you can only simulate U from a U m' f orm([0, 1]) distribution. Give the explicit function relating 6 to the simulated observation U