Q: Consider the function f(x) = (e^-|x|)/2 for x belonging to Real numbers. Prove that f is a density function.
For f(x) to be classified as a density function there are 2 things required:
1. f(x) >= 0 for all x belonging to Real numbers.
2. Indefinite Integral f(x)dx = 1.
Property 1 is simple enough to prove as f(x) >= 0 for all values of x. However, I am stumped on proving property 2. As far as I can tell, the integral is undefined. Am I going about the solution of this question all wrong or is there something else that proves a density function?