Raw Moment of Bernoulli Distribution/Proof 1

Proof
From the definition of expectation:


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

From the definition of the Bernoulli distribution:


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