Proving the Validity of a Bernoulli Distribution Probability Function

pyro_peewee
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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?
 
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Best place to start is writing down the definitions
 

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