My Math Forum  

Go Back   My Math Forum > College Math Forum > Advanced Statistics

Advanced Statistics Advanced Probability and Statistics Math Forum


Reply
 
LinkBack Thread Tools Display Modes
June 30th, 2007, 09:03 PM   #1
Member
 
Joined: Mar 2007

Posts: 57
Thanks: 0

coin tossing problem/ markov chain problem

The following two problems, if I'm right, are equivalent. I got an answer of 11/25 but I'm not sure. I drew a tree diagram (didn't have to but I found that simpler) and then used first step analysis.





a markov chain problem:

Let { X_t }_t>=0 and { Y_t }_t>=0 be two markov chains each with state space S = { 0,1 } and transition probabilities
P(0,0) = P(0,1) = P(1,0) = P(1,1) = 1/2
Both chains started in state 0 at time t=0.

Denote
C_t = I_{ t : X_t = X_t-1 = 1 } ( t )
D_t = I_{ t : Y_t = Y_t-1 = 1 } ( t )

where I is the indicator function

and denote

A = inf { t : C_t = 1 }
B = inf { t : D_t = 1 }

What is the probability that B < A ?








a coin tossing problem:

Two fair coins, coin X and coin Y, are tossed together, repeatedly.
Let
A = the event that (the first time that) 2 heads come up in a row from coin X
B = the event that (the first time that) 2 heads come up in a row from coin Y

What is the probability that event B occurs before event A?








my working:

using the context from the second problem, let:
P = probability of B before A
Q = P given that a head came up in the previous roll from coin X, while a tail came up in the previous roll from coin Y

then
Q = P/4 + (1/2 + P/4 + Q/4)/4
Q = (5P+2)/15

P = P/4 + Q/4 + (1/2 + P/4 + Q/4)/4 + (1/4 + P/4)/4
P = 11/25

Please correct me if I'm wrong. Thanks!
aptx4869 is offline  
 
Reply

  My Math Forum > College Math Forum > Advanced Statistics

Tags
chain, coin, markov, problem, problem or, tossing



Search tags for this page
Click on a term to search for related topics.
Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Coin tossing problem baxy Advanced Statistics 5 December 30th, 2013 05:34 PM
Markov Chain problem 450081592 Advanced Statistics 1 March 6th, 2012 04:17 PM
Coin tossing problem I have trouble understanding fibonacci Advanced Statistics 7 December 28th, 2011 10:07 AM
Coin tossing nikov Algebra 3 April 28th, 2009 03:32 AM
Coin tossing krackwacker Advanced Statistics 5 November 6th, 2008 07:17 PM





Copyright © 2019 My Math Forum. All rights reserved.