STA3007_0506_t02

STA3007_0506_t02 - STA 3007 Applied Probability Tutorial 2...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
STA 3007 Applied Probability 2005 Tutorial 2 1. Introduction to Markov Chain (a) Exercise i. Consider the problem of sending a binary message, 0 or 1, through a signal channel consisting of several stages, where transmission through each stage is subject to a fixed probability of error α . Suppose that X 0 = 0 is the signal that is sent and let X n be the signal that is received at the n th stage. Assume that { X n } is a Markov Chain with transition probabilities P 00 = P 11 = 1 - α and P 01 = P 10 = α , where 0 < α < 1 . (a) Determine Pr { X 0 = 0 , X 1 = 0 , X 2 = 0 } , the probability that no error occurs up to stage n=2. (b) Determine the probabilty that a correct signal is received at stage 2. 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2. Transition Probability Matrices of a Markov Chain (a) n - steps transition probabilities of a Markov Chain: We want to know P ( n ) ij = Pr { X m + n = j | X m = i } P ( n ) = PPPPP. ..P = P n Proof: P ( n ) ij = Pr { X n = j | X 0 = i } P ( n ) ij = X k =0 Pr { X n = j, X 1 = k | X 0 = i } ( Law of Total Probability
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/21/2011 for the course STA 3007 taught by Professor Kb during the Spring '11 term at CUHK.

Page1 / 4

STA3007_0506_t02 - STA 3007 Applied Probability Tutorial 2...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online