Consider a binary Markov chain with initial state probabilities $1$

$10$ and $9$

$10.$ The state transition

probabilities are $1$

$2$ and $1$

$2.$

$($i$)(5\%)$Find the initial$-$state entropy.

$($ii$)(10\%)$ Find the steady$-$state entropy.

$($iii$)(10\%)$ Find the entropy rate of the process.