Binomial(n, p) is the probability distribution of the number of "successes" in n independent trials whereby each trial has a binary outcome ("success" or "failure") with the "success" probability p.

If n is large and p is close to 0, then Binomial(n, p) can be approximated by a Poisson(λ) distribution with λ=np.

If n is large and p is far from 0 or 1, then Binomial(n, p) can be approximated by a Gaussian distribution with mean np and variance np(1-p).

@0foldcv Hey I know about that! I learned it from the Universe! :D

@0foldcv I didn't know about the approximations with others though, thanks! :D

@codepuppy The Gaussian approximation follows from the Central Limit Theorem, because a binomial(n,p) random variable X is a sum of n coin tosses.

However, I just learned about the Poisson approximation yesterday; it follows by taking the limit n to infinity of P(X = k) when the product np=λ is kept constant as n goes to infinity (i.e. p goes to 0 at a certain rate).

@0foldcv Oh cool! :D

The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!