Random Walk Returns
A particle starts at 0 on the integer number line. At each step it moves +1 or -1 with equal probability. What is the expected number of steps to return to 0 for the first time?
Related problems & prerequisites
Worth solving first
- Gambler's Ruin 6.0/10
- Ant on a Cube 5.0/10
- Coupon Collector 4.0/10
Source: Polya's recurrence theorem for random walks (1921). Statement written for AxiomIQ.