helpa$)$ Modems networked to a mainframe computer system have a limited capacity.

$\frac{4}{7}$ is the probability that a user dials into the network when a modem

connection is available, and $\frac{1}{4}$ is the probability that a call is received when

all lines are busy. The system can be considered as a binary Markov chain.

i$)$ Draw the state transition diagram of the Markov chain.

ii$)$ Find the state transition matrix and the probability state vector $p(k).$