## Problem of the Day #223: A Not-So-Random WalkOctober 28, 2011

Posted by Billy in : potd , trackback

Albert is currently located at the number $0$ on the number line. Every turn, Albert has a $\frac{1}{x}$ chance of moving one unit in the positive direction and a $1-\frac{1}{x}$ of standing still, where $x$ is the number Albert is currently on. What is Albert’s expected distance from the origin after $20$ moves?