Hosted by The Math Forum

Problem of the Week 1236

A Shrinking Random Walk

_____________________________________________
MacPoW Home ||  Forum PoWs ||  Teachers' Place ||  Student Center ||  Search MacPoW
_____________________________________________

Consider a random walk in the plane that starts at the origin and moves only in the positive x and positive y directions. The direction choice at each step is governed by the flip of a fair coin. The length of the first move is √2; the length of the second move is √2/2; the length of the third move is √2/4; and so on.

At the end of infinitely many steps, what is the expected distance from the origin?

Source: Tom Yuster, Math Horizons, April 2017, pp. 32-33.

[View the solution]

[Privacy Policy] [Terms of Use]

_____________________________________
Home || The Math Library || Quick Reference || Search || Help 
_____________________________________

© 1994- The Math Forum at NCTM. All rights reserved.
http://mathforum.org/


6 April 2017