# Bombing London (Poisson distribution) ## Bombing London 537 flying bombs fell on London during WWII. The British wanted to know if they were fired at random targets or not. The dissected the city into 576 areas of 1/4 square km each. $M_k$ counted the number of areas got hit by exactly $k$ bombs. | k | 0 | 1 | 2 | 3 | 4 | 5 | | ----- | --- | --- | --- | --- | --- | --- | | $M_k$ | 229 | 211 | 93 | 35 | 7 | 1 | The Poisson distribution for $\lambda =537/576$ predicts the following distribution | k | 0 | 1 | 2 | 3 | 4 | 5 | | ------------- | ----- | ----- | ---- | ---- | --- | --- | | $M\times P_k$ | 226.7 | 211.4 | 98.5 | 30.6 | 7.1 | 1.6 | The similarity of the two tables suggest the bombs were random and not target specific areas. Otherwise, it might be suspected that German agent are living in those area they were not bombed. Reference: [[@What is Random? Chance and Order in Mathematics and Life]] ## Created 2025-02-28 15:58