NAME: 3 An individual possesses 5 umbrellas which he employs in going from his home to office, and vice versa. At the beginning of a day if it is raining, then he will take an umbrella with him to the office, provided there is one to be taken. Similarly, at the end of a day if it is raining, chou he will take an umbrella with him to home, provided there is one to be taken. If it is not raining, then he never takes an umbrella. Assume that, independent of the past, it rains at the beginning of a day with probability 0.2, and similarly it mains at the end of a day with probability 0.2. a Define a DTMC which can be used to determine the proportion of time that the in- dividual gets wet. (Note that he gets wet if it is raining, and all umbrellas are at his other location.) Clearty define the state space and give the transition probability matrix. DO NOT DO ANYTHING ELSE IIERE. I am NOT expecting you to rintermine the proportion of time that the individual gets wet.(10 points)