Question: Define the Manhattan distance between two points A(Ax, Ay) and B(Bx, By) in a two dimensional space as |Ax Bx|+|Ay By|, denoted by d(A, B).

Define the Manhattan distance between two points

Define the Manhattan distance between two points A(Ax, Ay) and B(Bx, By) in a two dimensional space as |Ax Bx|+|Ay By|, denoted by d(A, B). A point is chosen uniformly at random inside a square with each side of length 2. The vertices of the square are on the x or y axis and the centre of the square is at the origin (see the figure below). Let L be the Manhattan distance from the point to the centre of the square (the origin O).

1. What is the CDF of L? 2. What is the PDF of L? 3. What is expected value of L? 4. What is the variance of L?

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