Expectation of Bernoulli Distribution/Proof 1

Proof
From the definition of expectation:


 * $\displaystyle \expect X = \sum_{x \mathop \in \Img X} x \, \map \Pr {X = x}$

By definition of Bernoulli distribution:


 * $\expect X = 1 \times p + 0 \times \paren {1 - p}$

Hence the result.