A traffic light at a busy intersection has a camera that monitors for cars that are speeding and for cars that driye through a red light. Each time it detects either occurrence. it generates an automatic infringement notice to be sent to the registered address of the offending car. The relationship between the number of speeding infringements [X] and red light infringements [Y [I that the camera generates on any given day can be described by the joint probability distribution below. Assume that the infringements generated are independent from day to day. Red Light (3;) 2 4 5 8 10 3 0.02 0.07 0.03 0.00 0.05 Speeding 7 0.06 0.04 0.06 0.07 0.05 (m) 8 0.02 0.03 0.04 0.09 0.03 10 0.03 0.05 0.07 0.08 0.04 A. [4 marks] Calculate the variance of the quantity W. B. [3 marks] L'Jn a given day, if the total combined number of infringements generated by the camera was greater than 11. find the probability that more than B red light infringements were generated by the camera. 0. [3 marks] Over the next week {T days], find the probability that the product of the number of speeding infringements and red light infringements generated by the camera {i.e., X K Y] is greater than 25 but less than ?5 on either 3 or 4 days. D. [3 marks] Dyer the next 1'5 days, find the approximate probability that the camera generates more speeding infringements than red light infringements on more than 33 days