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An ant does a random walk in a two dimensional plane starting at the origin at time $0.$ At every integer time greater than $0,$ it moves one centimeter away from its earlier position in a random direction independent of its past. After $4$ steps, what is the expected square of the distance (measured in centimeters) from its starting point?

  1. $4$
  2. $1$
  3. $2$
  4. $\pi$
  5. $0$

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