Explain: Comparison and Conclusion

The Logic of Comparison

1. Model: We assumed a Poisson model (random hits).
2. Fit: We "fit" the model to the data by finding the best $\lambda$ (which we did in part c).
3. Predict: If the model is true, how many cells should have 0, 1, 2... hits? We calculated these numbers.
4. Evaluate: Do these predicted numbers look like the real numbers?

Poisson Clumping

A key insight from this problem is about human perception of randomness. When people think of "random" or "uniform", they often imagine a perfectly even spread (like a checkerboard). However, true randomness (Poisson process) involves clumping.

• The fact that 7 cells got hit 4 times might look suspicious to a layperson ("They are targeting those spots!").
• But our calculation shows that in a purely random scenario with this density, we expect about 7 cells to be hit 4 times.
• Therefore, the clusters are not evidence of targeting; they are just a natural feature of randomness.

Conclusion

The fact that Observed $\approx$ Expected validates our initial assumption: The bombing was effectively random. This was a useful military intelligence finding. It meant the Germans didn't have the accuracy to target specific small neighborhoods in this area; they were just aiming at "London" generally.