This is because it is an exact solution if the random variable added at each step is not a Gaussian random variable but rather a binomial random variable with parameter n = 2.
2.
*The probability generating function of a binomial random variable, the number of successes in " n " trials, with probability " p " of success in each trial, is
3.
*The probability generating function of a negative binomial random variable on { 0, 1, 2 . . . }, the number of failures until the " r " th success with probability of success in each trial " p ", is
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