Question 2 (10 marks) a) An investment manager analyses three investment projects, say Project A, Project B and Project C. Let X, Y and Z be the returns from Project A, Project B and Project C over the next year, respectively. Assume that X follows a normal distribution with mean 0.1 and variance 0.2", (i.e., X ~ N(0.1, 0.23)); Y follows a normal distribution with mean 0.05 and variance 0.32, (i.e., Y ~ N(0.05, 0.32)); and Z follows a normal distribution with mean 0.04 and an unknown variance o', (i.e., Z ~ N(0.04, 0')). Also, assume that X, Y and Z are independent to each other. Based on these assumptions, answer the questions in (i)-(iii) as follows: (i) Write down the probability distribution for X - Y. (1 mark) (ii) Calculate the probability P(X > Y). (2 marks) (iii) Suppose the annualized returns for 6 trading days are obtained as a set of sample data for project C, as shown below: {0.01, 0.06, 0.18, 0.02, 0.07, -0.1} Suppose the returns of project C on different trading days are independent and identically distributed (i.e., Z; ~ N(0.04, o?), i = 1, 2, ...,6). Calculate the probability P(Z > 0.05), where Z = 12, Zi (2 marks)