Question 1: (a) Mark and Lisa are two real estate agents. Let X and Y be the respective numbers of houses sold by them in a week. Based on past sales, the following joint probabilities for X and Y are estimated. X 0 'l 2 0 0.00 0.4-5 0.06 >- 1 0.23 0.05 0.04 2 0.05 0.02 0.01 (i) Calculate the covariance between the houses sold by Mark and Lisa and interpret your nding. {4 marks) (ii) Determine whether the houses sold by Mark and Lisa are statistically independent. {3 marks) (iii) Find the expected value of total houses sold in a week by Mark and Lisa together. {4 marks) (b) The attendance at football games at a certain stadium is normally distributed, with a mean of 44,000 and a standard deviation of 3000. For a given game, what is the probability that the attendance will be between 45,000 and 49,000? (4 marks)