You are working as a computer scientist in a company that manufactures smart phones. There has been a malfunction in the production line that has caused an issue in some of the phones which prevents them from turning on. You are asked to investigate the proportion (Ø) of the faulty phones. You randomly choose 30 phones from which three of them do not work. Assume a uniform prior for Ø. a. Compute the posterior of Ø. b. Which one of the following models is favourable? Mo x1, x2,..., 30/0~ Bern(5%) M₁: 1, 2, x300~ Bern(o), where ~ Beta(a, 3) Bayes factor (BF1,2) Interpretation BF < 100 Decisive evidence for M2 Strong evidence for M₂ BF < 10 < BF < 1⁰ < BF <1 1 < BF <3 3 < BF < 10 Moderate evidence for M₂ Weak evidence for M₂ Weak evidence for M₁ Moderate evidence for M₁ Strong evidence for M₁ Decisive evidence for M₁ BF > 10 BF > 100
