Question 3. (6 marks). Imagine that you have created a machine learning model whose purpose is to detect and predict fraudulent transactions at a bank. From previous data, you estimate that 1.5% of transactions are fraudulent. By applying test data to your model, you estimate that it correctly identies 85.3% of fraudulent transactions as fraudulent, and correctly identies 97.5% of legitimate transactions as legitimate. Let F denote the event that a transaction is actually fraudulent, and let I denote the event that a transaction is identied as fraudulent by the model. Assume that a positive instance refers to a fraudulent transaction. (a) (b) (C) (d) (9) (f) (s) Based on the information described above, state the probabilities P[F), PU | F) and PH\" | F"). According to the reading materials, the probability PU | F) is called the true positive rate. \"lhat name is given to the probability PU" | F\")? Determine PU\" | F} and PH | F\"). Hint: apply complements. According to the reading materials, what names are given to these probabilities? Use the Law of Total Probability to calculate the probability that a transaction is identied as fraudulent. Use Bayes' Theorem to calculate P(F | I) and P(F"' | I '1). According to the reading materials, what names are given to these probabilities? Determine PUT\" | I) and PIZF | 1\"). According to the reading materials, what names are given to these probabilities? Suppose that a colleage has used your model and it has identied 200 transactions as fraudulent. Your colleage suggests that, based on the false positive rate, they should expect approximately 29 or 30 of these to be legitimate transactions. Is your colleague's line of reasoning correct? If so, explain why. If not, explain a more suitable line of reasoning, including a correct description of the expected number of legitimate transactions. Complete Question 3 by hand, showing all working. Give your answers to at least 3 decimal places