 We are interested in \(X(t+1)\) and \(p(t+1)\), the number of copies and frequency of the allele in generation \(t+1,\) respectively. (They are related by \(p(t+1) = \frac{1}{2N}X(t+1).\)) Now, \(X(t+1)\) is a random variable that can take any of \(2N+1\) possible values from the set \(\{0, 1, 2, \ldots ,2N\}\). Since the offspring generation is formed by random sampling from the parental gamete pool, the probability distribution of \(X(t+1)\) is given by the binomial distribution: