A source emits symbols 0 and 1 for transmission to a sink. Random noises S 1 , S 2 …successively and independently affect the transmission process of a symbol in the following way: if a '0' ('1') is...

A source emits symbols 0 and 1 for transmission to a sink. Random noises S₁, S₂
…successively and independently affect the transmission process of a symbol in the following way: if a '0' ('1') is to be transmitted, then S_i
distorts it to a '1' ('0') with probability p (q); i = 1, 2, ... Let X₀
= 0 or X₀
= 1 denote whether the source has emitted a '0’ or '1' for transmission. Further, let X_i
= 0 or X_i
= 1 denote whether the attack of noise S_i
implies the transmission of a '0' or a '1', i = 1, 2, ... The random sequence {X₀, X₁, ...} is an irreducible Markov chain with state space Z = {0, 1} and transition matrix

(1) Verify: On condition 0 <>

(2) Let p = q = 0.1. The transmission of the symbols 0 and 1 is affected by the random noises S₁, S₂, ..., S₅.

Determine the probability that a '0' emitted by the source is actually received.