0:00
Probability 9.8/10

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

Source: Polya's recurrence theorem for random walks (1921). Statement written for AxiomIQ.