Geometric Distribution Rules

Question

I am hoping someone could please clarify the rules for the Geometric Distribution.

I know that if $X$~$Geo(p)$ :

$P(X=r) = p * (1-p)^{r-1}$

$P(X < a) = (1-p)^a$

What are the rules for $P(X \ge x), P(X > x)$ and $P(X \le X)$ ?

Answer 1

Hints:

$X\ge x$ is the complement of $X<x$.

$X\le x$ is the same (for this discrete distribution) as $X<x+1$.

$X > x$ is the complement of $X\le x$.