Hi guys. Although Martingales seem to be easy and I work with them daily, I'm having trouble with the following problem. Could anyone help me with the demonstration?Consider the Polya urn containing a red and a blue ball initially. At each time n=1,2,3...., a ball is drawn and after noting the color, the ball is placed back into the urn along with another ball of the same color. So after n draws, the urn has n+2 balls. Let Yn be the number of blue balls in the urn and let Xn = (Yn/(n+2)). Show that Xn is a martingale with respect to Fn = sigma{Yk : k<n}Thanks in advance!

Maybe I'm too stupid this morning but hey, what I've got to looseMy two cents:It's easy to check thatE(X_{n+1}|F_n)=X_nTherefore for any n>mE(X_{n}|F_{m})=E..E(E(X_{n}|F_{n-1})|F_{n-2})....|F_{m})=E..E(E(X_{n-1}|F_{n-2})....|F_{m})= ... =X_mQEDHTH

Thanks a lot for your help, pjakubenas. That should work.