Random Walk Mean After Twenty Steps

Each step has expected value 0 by symmetry.

Use linearity of expectation over all 20 steps.

1. 1. Apply linearity

   The position after 20 steps is $S_{20}={\sum }_{i=1}^{20}{X}_i$ with $E[X_i]=0$.

   $$E[S_{20}]=\sum _{i=1}^{20}E[X_i]=0$$

Answer: 0