A geometric distribution formula is:
p*(1-p)^(n-1)

Where p = probability of success
and n = is the observed value of success.

What does the (1-p)^(n-1) represent?

Cleaner equation posted below:

Question

A geometric distribution formula is:
p*(1-p)^(n-1)

Where p = probability of success 
  and   n = is the observed value of success.

What does the (1-p)^(n-1) represent?

Cleaner equation posted below:

mhchen · Answer

$$P(Y=k)=(1-p)^{k-1}p~~~~~~~~~~~~~~(1-p)^{k-1}  <- represents?$$

holsteremission · Answer

$p$ is the probability of success, so $1-p$ is the probability of failure. This means $(1-p)^n$ is the probability of failing $n$ times (consecutively).

So what the formula describes is the probability of one success after $n-1$ failures.

mhchen · Answer

O_o wow...

mhchen · Answer

Why is it to the power of n-1 though. Instead of just 'n'? Because 0 can't be included or something?

holsteremission · Answer

For a geometrically distributed random variable $X$, being interested in the value of $\mathbb P(X=k)$ translates to asking "What is the probability that whatever I'm observing actually occurs for the first time on the $k$th trial?"

For something to happen on the $k$th trial for the first time would be that it *has not* happened for the previous $k-1$ trials.

mhchen · Answer

ah, okay. ty

holsteremission · Answer

yw