Finding Expected Value of a Double-Exponential Distribution

[corny1355]

Homework Statement

The random variable X has a double-exponential distribution with parameter p>0 if its density is given by

f_x (x) = (1/2)e^(-p|x|) for all x.

Show that the expected value of X = 0.

Homework Equations

I know that the expected value of a random variable x is

∫ x * f(x) dx

The Attempt at a Solution

We are told that f_x (x) = (1/2)e^(-p|x|)

So I'm guessing you have to do the following integral going from 0 to infinity:

∫ x * (1/2)e^(-p|x|) dx

But I'm unsure about how to compute this integral.

 

[Galileo]

If your sample space is [0,\infty), how could the average value of X be 0?
Also, there wouldn't be a need for absolute values if x couldn't be negative.
I`m sure that the problem implicitly assumes that X can take all values in R.

You could evaluate the integral by splitting it in two pieces.
There's a faster way though. Maybe drawing the graph of f will help.