MathDB

Suppose you are given a fair coin and a sheet of paper with the polynomial

x^m

written on it. Now for each toss of the coin, if heads show up, you must erase the polynomial

x^r

(where

r

is going to change with time - initially it is

m

) written on the paper and replace it with

x^{r-1}

. If tails show up, replace it with

x^{r+1}

. What is the expected value of the polynomial I get after

m

such tosses? (Note: this is a different concept from the most probable value)

Problem Statement