Proving the Validity of a Bernoulli Distribution Probability Function

[pyro_peewee]

I'm just curious as to how to prove that a Bernoulli distribution probability function is valid (ie. that it is indeed a probability distribution function). I have a hunch that all we do is add up all of the probabilities associated to every x value, but I'm not sure. Can someone confirm this? Can someone show me how?

 

[bpet]

Best place to start is writing down the definitions