British Travel Agency has asked a junior manager to investigate flight delays during the week before Christmas at Heathrow Airport. The random variable X is the number of flights delayed per hour. The results are shown in the following table. x 0 1 2 3 4 5 6 7 8 9 p(x) 0.10 0.08 0.07 0.15 0.12 0.08 0.10 0.12 0.08 0.10 a) Show that the probability distribution is well defined and derive the cumulative probability distri bution. [4 marks] b) Find the probability that there would be three through seven (inclusive) delayed flights per hour? [2 marks] c) Find the mean and variance of flights delayed per hour. [4 marks]