I am confused with the pdf of the exponential distribution,
Some of the times, the pdf is shown as :
$f(x)=\lambda e^{-\lambda x},\ x \ge 0$
while sometimes it is shown as
$f(x)=e^{-\lambda x},\ x \ge 0$
Are there any differences between them?
Edit:
$f(x)=\lambda e^{-\lambda x}$ for $P(X<x)$
$f(x)=e^{-\lambda x}$ for $P(X>x)$
Further question:
What about $1-\lambda e^{-\lambda x}$ ? Is this the cdf for $P(X<x)$ or $P(X>x)$?