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.

Go to the list of words starting with: a b c d e f g h i j k l m n o p q r s t u v w y z