# What is the probability density function?

• Mar 16th 2010, 05:55 PM
AlphaRock
What is the probability density function?
f(x) = 5e^(ax) for x >= 0.

Find a so that f(x) is a probability density function.

My work:

I can only get up to
(5/a) lim [(e^at)-1] = 1
t-> infinite

Don't really know what to do after, but i think a has to be negative so that e^at can approach 0.
• Mar 16th 2010, 05:59 PM
Moo
Yes, a has to be negative. And if so, while t goes to +infinity, the limit of $e^{at}$ is 0. Which should give you the solution for a...