Deduce from the previous questions that $$\sum _ { k = 0 } ^ { n } \left( x - \frac { k } { n } \right) ^ { 2 } \binom { n } { k } x ^ { k } ( 1 - x ) ^ { n - k } = \frac { x ( 1 - x ) } { n } .$$
Deduce from the previous questions that
$$\sum _ { k = 0 } ^ { n } \left( x - \frac { k } { n } \right) ^ { 2 } \binom { n } { k } x ^ { k } ( 1 - x ) ^ { n - k } = \frac { x ( 1 - x ) } { n } .$$