Question 2 [20 marks] (a) Noriko, a young woman who attends funerals to avoid getting picked up by men. Given that the probability she attends one funeral on a day is 0.5, and zero probability of attending more than one funeral or visits Meshiya more than once in a day. (i) Let X be the number of funerals she attends on Monday and Tuesday and Y be the number of funerals she attends on Wednesday and Thursday. Find Var (X + Y). [5 marks] (ii) If she attends a funeral on a day, the probability that she will order Barbecue Special (one of the items in the secret menu) is 0.7. She will not order this item if she doesn't attend any funeral. On one particular week, let M be the number of funerals she attends from Monday to Friday, and A be the number of days she orders Barbecue Special in these five days. Find E(M + N). [5 marks] (b) Seita and Saori want to meet at Meshiya around 2:00 am. Given that Seita arrives at a time uniformly distributed between 1:30 am to 2:30 am and Saori independently arrives at a time uniformly distributed between 1:45 am and 2:15 am. Find the probability that (i) both of them arrive there before 2:00 am, given that Seita arrives after 1:45 am. [5 marks] (ii) the first to arrive waits no longer than 5 minutes. [5 marks]