As stated in the article binomial distribution by britannica.com the binomial distribution was used by Jakob Bernoulli when he said that "the probability of $k$ ... outcomes in $n$ repetitions is equal to the $k$th term ... in the expansion of the binomial expression $(p + q)^n$, where $q = 1 − p$" (quote from this article).

My question: Is it right to say that Jakob Bernoulli is the inventor of the binomial distribution or was this distribution already used before? I guess he's the first one who uses the skewed binomial distribution but I am not sure whether the symmetric binomial distribution is used before or not.

What I have found out: For example Blaise Pascal investigated the problem of points (together with Fermat). In this problem one has to decide how to split the stakes of a game when a game is interrupted before it ends. Pascal proved that if person A needs $r$ points and $B$ needs $s$ rounds to win, the stakes should be split as

$$\sum_{k=0}^{s-1} \binom{r+s-1}{k} \text{ to } \sum_{k=s}^{r+s-1} \binom{r+s-1}{k}$$

Currently I read "A history of Probability and Statistics and their Applications before 1750" by Anders Hald but it is not clear to me whether Pascals knows the symmetric binomial distribution or not.


1 Answer 1


See Stigler history of Statistics, p. 92 in which the binomial comes from, Pascal, Newton, Bernoulli, and De Moivre in that order. Hth Best!


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