# Forgetful Burglar

Forgetful Burglar

A forgetful burglar wanders up and down one side of an infinitely long street to visit homes. He is so absorbed in his burgling that he forgets from which direction he entered a particular house and which houses on the street he has already entered. If he is so unfortunate as to re-enter a house, the already aroused occupants detain him to his permanent disadvantage.

Assume then that the burglar repeatedly takes, with equal probability, a step of length , , …, , , , , …, , or . If he visits a home again, his walking stops. The Demonstration shows sample paths of the forgetful burglar and relative frequencies of the length of his path over 1 million simulated paths, both for .

-n

-(n-1)

-2

-1

1

2

n-1

n

n=1,2,…,10