6 of 31 + 80% 4. (a) An indicator of the value of a stock relative to its earnings is its price-earnings ratio. The following table provides the summary statistics of the price-earnings ratios for a random sample of 24 stocks, 8 each from the healthcare, financials and real estate sectors. Sector Sample mean | Sample variance | Sample size Healthcare 32.65 4.23 Financials 30.01 3.64 00 00 00 Real estate 29.24 4.27 You are also given that: 8 IF = 22,657.84. Test at the 5% significance level whether the true mean price-earnings ratios for the three market sectors are the same. Use the ANOVA table format to summarise your calculations. You may exclude the p-value. (10 marks) (b) Consider two random variables X and Y which both take the values 0, 3 and 6. The joint probabilities for each pair are given by the following table: X -0 X -3 X=6 Y -O 0.12 0.08 0.20 Y - 3 0.10 0.06 0.14 Y - 6 0.08 0.06 0.16 i. Calculate P(Y - 3 | X > 2). (4 marks) ii. Define U - X and V = |Y - 3). Calculate the covariance of U and V. (6 marks) MAY