Q$2$: Gillbert$-$Elliott model application

We have two sensor nodes that share a wireless channel. The state of the channel follows the Gillbert$-$Elliott model. Suppose that the transition probabilities in Fig$\mathrm{.}3\mathrm{.}7\mathrm{.}1$ are $\backslash ($ p$=10^\{-5\}\backslash )$ and $\backslash ($ r$=10^\{-1\}\backslash ).$

$($a$)$ Find the average length of an error burst.

$($b$)$ Obtain the average length of an error$-$free sequence of message transmission.

$($c$)$ Assume that the error probability in Good and Bad states is negligible and almost sure, respectively. Compute the average message loss rate of the channel.