1. Flying Bomb Hits - In June 1944 during the second World War the Germans launched a much feared secret weapon - a small, pilotless, jetpropelled plane carry- ing a ton of explosives that detonated on contact. The Germans called it the V1 - the British called it the flying bomb. The British authorities were anxious to know if these weapons could be accurately aimed at a particular target, or whether they were landing at random. In analyzing hits in the south of London, investigators partioned the area into 576 small sectors, each being - of a square kilometer. A careful counting of the hits produced the table below. Number of sectors with exactly k hits k sectors 0 229 1 211 2 93 3 35 4 7 5+ What might you lead you to expect that a Poisson distribution might be a good model for the number of hits on each sector? Fit a Poisson distribution to the data by taking A to be the average number of hits per sector. Use this A to compute the theoretical frequencies of 0, 1, 2, 3, 4 and 5 hits in 576 sectors. What can you say about the targeting process? 2. Flight Overbooking - Airlines regularly overbook their flights. PQ Airways has confirmed 400 passengers on its flight 999 to London but its A-380 is configured to carry only 396 passengers. The probability of a passenger with a confirmed seat not showing up is 0.01. (Assume passengers behave independently.) PQ Airways MacBook Pro G Search or type URL + % & * 5 6 7 9 O R T Y U O P G H C K L