Question 2 A college student union is organizing a fund raising. A total of 285 tickets are sold, each at $50. The student union has got sponsors from different parties, below are the list of all prizes: 1\" prize: A Caribbean cruise holiday, values $2000 2"d prize: Supermarket spending coupons, values $1000 3'7d prize: Movie tickets, values $300 4'11 prize: Restaurant spending coupons, values $300 Others: A thank you card, values $0 (a) Use X to represent the earning of a person who has bought one ticket. Present the probability distribution function of X. (Earning = the value of the prize the selling price of the ticket) (4 marks) (b) Calculate the expectation and standard deviation of X. (4 marks) (c) Kevin bought three tickets. He says the number of prizes he may win with his tickets follow a Binomial distribution, Y ~ Bin(3, ). Is he correct? (Answer: Yes I No, no explanation is required in part (c)) (2 marks) (Total: 10 marks)