Question

coocoo and bird each start with $2013 and are flipping a fair coin. When the coin comes up heads coocoo pays bird $1 and when the coin comes up tails bird pays coocoo $1. Let f(n) be the number of dollars coocoo is ahead of his starting amount after n flips. Compute the expected value of max{f(0),f(1),f(2),...,f(2013)}.

Answer 1

looks hard

Answer 2

don't ask me how
\[\frac{ -1 }{ 2 }+\frac{ \left( 1007 \right)\ \left(\begin{matrix}2013 \\ 1006\end{matrix}\right) }{ 2^{2012} }\]

Answer 3

Wouldnt even know where to start with that one. Not the typical expected value problem Im used to seeing, lol.

Answer 4

\[\Gamma=\sum_{i=0}^{\infty}i \times P(\max profit =i)=\sum_{a=1}^{2013}P(\max profit \ge a)\]

Answer 5

Lol, thats some stats unlike Ive ever seen. Cant just be a simple expected value D:

Answer 6

35.3