a) 60% of the population of the Middle Earth are smokers. In addition, 80% of the smokers and 30% of the non-smokers suffer from stress. Answer the following. i) What

percentage of Middle Earth's population suffer from stress? ii) If a randomly chosen person from Middle Earth suffers from stress, what is the probability that the person is a smoker? iii) Using an appropriate test for independence, show whether in Middle Earth the events A={a person is a smoker} and B={a person suffers from stress} are independent or not. b) 100 tickets are sold in a lottery in which there is one top prize of £50 and four prizes of£10 each. Each ticket costs £1. Let X be your net gain (or loss) when you buy one ticket (net gain: winnings after deducting any costs). i) Compute the probability mass function of X. ii) Compute the expected value of X. iii) How much should the top prize be for the expected value of X to be 0.50 (50 p)? c) A Naïve Bayes classifier uses only 2 features, f1 and f2, to classify items into three classes: A, B and C. For each statement below state whether it is True or False and explain why (no explanation, no marks). i) P(A | f1), P(A | f2) are learnt during the training phase. ii) The naive assumption in Naïve Bayes classification is that f1 and f2 occur independently of each other only in class A. iii) P(A), P(B), P(C) are learnt during the training phase. iv) Based only on P(A | f1, f2) > P(B | f1,f2) the classifier will classify an item in class A.