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I know that the expectation E(S_{n}) for a one-dimensional simple random walk is zero. But what about the variance?

I read in http://en.wikipedia.org/wiki/Random_walk#One-dimensional_random_walk" that the variance should be E(S_{n}^{2}) = n.

Why is that? Can anyone prove it?

Thank you very much!

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# Variance in Random Walk

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