In doing a problem, I considered N (a large number, in the range 100,000-1,000,000) raindrops, falling into A (fixed at 100) segments on a roof, distributed using a random number generator I programmed. In considering the number of raindrops that fell into a given segment, the average would be [tex]\mu=\frac{N}{A}[/tex]. For a fixed N, I calculated the standard deviation [tex]\sigma[/tex]. I then plotted the standard deviation against the average, and found a nearly perfect relationship [tex]\sigma = \sqrt{\mu}[/tex]. Is this relationship correct? Can anyone tell me why it would be so, or give me a starting point to show it?(adsbygoogle = window.adsbygoogle || []).push({});

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# Large numbers and standard deviation for a uniform distribution

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