An inventory Model: $(q,Q)$ policy

Suppose that random variables ${}_n($demand$)$ have the

following probability distribution:

a$)$ What is the domain of $x_n?$

b$)$ Find the following probabilities

i$.P\{x_{n+1}=1|x_n=4\}$

ii$.P\{x_{n+1}=3|x_n=2\}$

iii. $P\{x_{n+1}=4|x_n=1\}$

iv$.P\{x_{n+1}=2|x_n=0\}$

C$)$ Determine the transition probability matrix of $x_n$