Expected Distance on a CircleCalculus Level 5
An angle \(\theta\) is chosen randomly in the interval \([0,2\pi )\), and its corresponding point on the unit circle is plotted. Let this point be \(P\). Now let \(A=(1,0)\) and \(B=(-1,0)\).
Let the expected value of \(PA+PB-2\) be \(E\).
What is \(\lfloor 1000E\rfloor\)?