The Average Position,or Expectation Value,of a Particle Whose Wave Function $\Psi$

Multiple Choice

The average position,or expectation value,of a particle whose wave function $\Psi$ (x) depends only on the value of x,is given by < x > =

A) $\int _ { - \infty } ^ { + \infty } \sqrt { x } \psi ( x ) d x$ .
B) $\int _ { - \infty } ^ { + \infty } x \psi ( x ) d x$ .
C) $\int _ { - \infty } ^ { + \infty } \frac { x } { 2 } \psi ^ { 2 } ( x ) d x$ .
D) $\int _ { - \infty } ^ { + \infty } \frac { x ^ { 2 } } { 2 } \psi ( x ) d x$ .
E) $\int _ { - \infty } ^ { + \infty } \psi ^ { * } ( x ) x \psi ( x ) d x$ .