4) Consider a particle to be constrained to lie along a one-dimensional segment 0 to a. The
probability that the particle is found to lie between x and x + dx is given by
$$p(x)dx = \frac{2}{a}sin^2{\frac{n\pi x}{a}}dx$$ Where n= 0,1,2,....
Show that average position of the particle along the line segment is $\frac{a}{2}$ that is $<x>$.
Show that $p(x)$ is normalized.
5) For the function in question (4) find $< x^2 >$, $\sigma^2$ and $\sigma$
