Problem $3$:

Consider that the three types of days exist "sunny", "rainy" and "cloudy". Every type of day is followed by

the same type of day with probability $0\mathrm{.}7.$ Every type of day is followed by different type of day with

probability $0\mathrm{.}15.$ Answer the following,

i$)$ Draw state diagram showing all probabilities.

ii$)$ What is the probability of having cloudy day after tomorrow if today is rainy day?

iii$)$ What is the probability of having rainy day after tomorrow if today is sunny day?

iv$)$ Find the steady$-$state probabilities.