Assume that you want to investigate the proportion () of defective items manufactured at a production line. A researcher takes at random sample of 36 items. Six were defective in the sample. Assuming a Jeffrey prior for , determine the posterior distribution of . (13 marks)

b. The researcher now tells you that he did not decide on the sample size before the sampling was performed. Her sampling plan was to keep sampling items until she had found six defective ones. Redo the posterior calculations this time under the new sampling scheme. Comment on the results.