Consider a typical random walk problem, where the probability to go right is $R$ and the probability to go left is $L$, where $R+L=1$. The particle can move 1 unit in each step, and starts at zero.
Let the particle move $n$ steps and write down its location away from zero.
Now repeat this a very large number of times.
What is the mean location of the particle from zero, and what is the standard deviation of the particle's location?