HMMT November 2019 U5

A point $P$ is chosen uniformly at random inside a square of side length 2 . If $P_{1}, P_{2}, P_{3}$, and $P_{4}$ are the reflections of $P$ over each of the four sides of the square, find the expected value of the area of quadrilateral $P_{1} P_{2} P_{3} P_{4}$.