Problem 4.9

A particle performs harmonic oscillations along the $x$ axis according to the law $x=a \cos \omega t$. Assuming the probability $P$ of the particle to fall within an interval from $-a$ to $+a$ to be equal to unity, find how the probability density $d P / d x$ depends on $x$. Here $d P$ denotes the probability of the particle falling within an interval from $x$ to $x+d x$. Plot $d P / d x$ as a function of $x$.