Geometric Distribution

Modeling the number of trials needed to get the first success.

"How Long Until It Hits?"

The Geometric distribution answers the question: "How many times do I have to try until I get my first success?" It models the number of independent Bernoulli trials required to achieve the first success.

In finance, this could model the number of trades you need to make until you have your first profitable one, or how many quarters it will take for a startup in your portfolio to finally turn a profit. It's always right-skewed, because a small number of trials is always more likely than a large number.

The Formula

The probability that the first success occurs on the

k

-th trial is:

P(X=k) = (1-p)^{k-1}p

$k$ is the number of trials (must be 1, 2, 3, ...).
$p$ is the probability of success on a single trial.

Interactive Geometric Distribution

Adjust the probability of success (

p

) to see how it affects the likelihood of achieving the first success on a given trial.

Probability of Success (p): 0.25