2
$\begingroup$

I need assistance with the following question:

The particle starts from the origin on the number line . It makes n steps at total. At each step it jumps with the probability 1/2 to the origin and with the uniform probability jumps to the one of its neighbors.I have to prove that the expectation of its maximal distance from the origin is proportional to logn

Thanks

  • 0
    This is very related to a project I was(and am) working on. http://www.artofproblemsolving.com/Forum/viewtopic.php?f=498&t=358543 has the details of the problem, perhaps you will get some ideas from there.. I would like to see some ideas that may help me too! haha2011-01-19
  • 0
    Also, in literature, these types of problems are called random walk with killing perhaps that will help you out too.2011-01-19

2 Answers 2