Paper 2, Section I, F

Consider a particle situated at the origin $(0,0)$ of $\mathbb{R}^{2}$. At successive times a direction is chosen independently by picking an angle uniformly at random in the interval $[0,2 \pi]$, and the particle then moves an Euclidean unit length in this direction. Find the expected squared Euclidean distance of the particle from the origin after $n$ such movements.

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