Expected Distance on a Circle

Calculus 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 \(\lfloor 1000E\rfloor\)?

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, interactive explorations.

Used and loved by over 7 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.