Variance of an asymmetric random walk

EasyRandom Variables Stochastic Processes~2m

A random walk takes independent steps that are $+2$ with probability $\tfrac12$ or $-1$ with probability $\tfrac12$ . What is the variance of its position after 10 steps?

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The steps aren't $\pm1$ - first find one step's variance via $E[X^2]-(E[X])^2$ .
Then variances of independent steps add: multiply by 10.

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Variance of an asymmetric random walk

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