Does this discrete probability distribution have a name?

Question

I was wondering whether the probability distribution

$$P(X = k) = \frac{\lambda}{(1+\lambda)^{k+1}}, \quad k= 0, 1, 2, \dotsc,$$

where $\lambda$ is a fixed positive number, has a name.

Answer 1

Geometric distribution. There is some slight terminology ambiguity explained in the wikipedia article. The customary parameter is $p = \lambda/(1+\lambda)$. (And not $1/(1+\lambda)$, as Peter Foreman points out.)