A quantum particle has a wave function
$$
\psi(x)=\left\{\begin{array}{ll}{\sqrt{\frac{2}{a}} e^{-x / a}} & {\text { for } x>0} \\ {0} & {\text { for } x<0}\end{array}\right.
$$
(a) Find and sketch the probability density. (b) Find the probability that the particle will be at any point where $x < 0 .$ (c) Show that $\psi$ is normalized and then $(\mathrm{d})$ find the probability of finding the particle between $x=0$ and $x=a$ .