Consider a random walk in the plane where each step is taken, beginning at the origin, in either in the positive x or positive y direction, i.e. either east or north, each choice being made by the flip of a fair coin. The length of each step is 1/2 the length of the previous step, and the first step has length √2. After infinitely many steps have been taken, what is your expected distance from the origin?

Edit: Ignore the original text in pink. Instead,

What is the distance to the origin of the centroid of the possible termination points? You find the centroid of a set of points by averaging respectively their x- and y- coordinates.

First correct answer wins, but style points will be awarded as well.

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## bonanova

Consider a random walk in the plane where each step is taken, beginning at the origin, in either in the positive

xor positiveydirection,i.e. either east or north, each choice being made by the flip of a fair coin. The length of each step is 1/2 the length of the previous step, and the first step has length √2. After infinitely many steps have been taken, what is your expected distance from the origin?: Ignore the original text in pink. Instead,EditWhat is the distance to the origin of the centroid of the possible termination points? You find the centroid of a set of points by averaging respectively their

x-andy-coordinates.First correct answer wins, but style points will be awarded as well.

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