Solution
= Solution
The <probability density> is even, so its first moment vanishes. Its second moment follows by integrating the polynomial:
$$
\langle x^2\rangle=A^2\left[\frac{2a^7}{3}-\frac{4a^7}{5}+\frac{2a^7}{7}\right].
$$
Using the <normalization> from part <S3/2/a> gives
$$
\boxed{\langle x\rangle=0,\qquad\langle x^2\rangle=\frac{a^2}{7}.}
$$
The <variance> in <position> is consequently $a^2/7$.