1
$\begingroup$

I am learning about discrete probability distributions and found 2 definitions for Geometric Distributions from wikipedia: 1. The probability distribution of the number X of Bernoulli trials needed to get one success, supported on the set { 1, 2, 3, ...} 2. The probability distribution of the number Y = X − 1 of failures before the first success, supported on the set { 0, 1, 2, 3, ... }

It seems like a subtle difference, but i'm having trouble wrapping my head around when i would use which? Any insights appreciated.

  • 0
    I always thought about it like this: if the geometric random variable can assume $0$, then use $(1-p)^{n}p$. Else use $(1-p)^{n-1}p$. E.g. is it possible to have zero failures?2010-11-25
  • 0
    Geometric always means "the number of trials before the state changes", i.e. from success to failure or vise-versa, and you have to interpret it according to what is being described. Given the simplicity of the distribution, the one to which an author is referring is almost always obvious after a second of thought.2010-11-26

1 Answers 1