## random

The random variable $X$ has the Poisson distribution with mean $v$.

In this and the other theorems of this section, the $X_n$ are any independent random variables with a common distribution.

To calculate (2), it helps to visualize the $S_n$ as the successive positions in a random walk.

The proof shows that if the points are drawn at random from the uniform distribution, most choices satisfy the required bound.

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