marks. A machine is built to make mass-produced items. Each item made by the machine has à probability O of being defective. Given the value of 0, the items are independent of each other, where 0 is unknown and would like to estimate. Suppose ® has for prior distribution a Beta(a, 3) distribution, where a > 0 and B > 0. machine is tested by producing items until the first defective occurs. Suppose that the first 12 items are not defective but the y = 13th item is defective. ????Write down the likelihood function for 0 and find the MLE of e. ????Given the observed data y = 13, what is the posterior distribution of 0,