Probability or Martingale

fogsnow · March 30th, 2009, 8:18 am

There is a question, as shown in the follow figure.It require 3 methods.I just figure out the simplest one (list all possible paths then exploit the conditional probabilities to get the expection)I guess there should be one martingale method( I am not very familiar with that).anyone can help?thanks!

shinichivn · March 31st, 2009, 9:36 am

another method is to construct a transition prob matrix 9x9 for A_n

FalsePositive · September 21st, 2009, 6:13 pm

Can someone please solve this question using either methods? I want to learn this as I seem to have problems with transition matrix brainteasers.. Thanks,

MatthewM · September 21st, 2009, 9:58 pm

QuoteOriginally posted by: shinichivnanother method is to construct a transition prob matrix 9x9 for A_n The relevant matrix is 14x14, not 9x9. It involves both the state of X_n and A_n, but because the initial state X_0 is even, you can eliminate all odd values for A_nThe states you need to cover are (X_n, A_n):{(1,0),(1,2),(2,0),(2,2),(2,4),(3,0),(3,2),(3,4),(3,6),(4,0),(4,2),(4,4),(4,6),(4,8)}The transition matrix is relatively sparse; there are at most 3 non-zero entries on each row.