Talk:Moment Generating Function of Geometric Distribution

Per the :

$X$ has the geometric distribution with parameter $p$ :
 * $\map X \Omega = \set {0, 1, 2, \ldots} = \N$
 * $\map \Pr {X = k} = \paren {1 - p} p^k$

where 0 < p < 1.

I think we need to edit Moment Generating Function of Geometric Distribution as follows:

From: Let $X$ be a discrete random variable with a geometric distribution with parameter $p$ for some '''$0 < p \le 1$. '''

To: Let $X$ be a discrete random variable with a geometric distribution with parameter $p$ for some $0 < p < 1$.

Am I missing something? --Robkahn131 (talk) 13:38, 16 April 2021 (UTC)


 * Quite right. Good shout. --prime mover (talk) 16:45, 16 April 2021 (UTC)


 * The definition used on this page $\map \Pr {X = k} = \paren {1 - p}^k p$ is inconsistent with the definitions used on virtually all other pages


 * Official Definition.
 * $\map \Pr {X = k} = \paren {1 - p} p^k$


 * Expectation of Geometric Distribution
 * Variance of Geometric Distribution
 * --Robkahn131 (talk) 18:41, 16 April 2021 (UTC)


 * Take a look at Definition:Geometric Distribution which discusses this.


 * This page was written by someone obviously using a different source work from the one used for the definition as used on.


 * Please do not automatically assume that if a page says something different from what you find somewhere else that it is automatically wrong. There may be a context in which it is just different. I think this is one of those cases, where both definitions may need to be reconciled. Otherwise someone's going to read this page and say: idiot, everybody knows $\map \Pr {X = k} = \paren {1 - p}^k p$, and change it back to what it was.


 * The best approach is to document the result for both definitions. Clearly we need to bring both up to the correct specification so as to allow this to be done, but because of the stupidity, laziness and general worthlessness of the person who originally posted up this pile of garbage, they hid the alternative definition in a section stupidly and unforgivably titled "Note". The perpetrator will be taken out and shot. --prime mover (talk) 20:18, 16 April 2021 (UTC)