Q8.

8. A student moves from home to office in the morning and from office to home in the evening. The student has 5 umbrellas and takes an umbrella only when it rains. If there is no umbrella at the present location, the student gets wet. Assume that during each of the student's transitions it rains independently with probability p. a) What is the stationary probability that the student carries an umbrella at least once (1.6., from home>office, office> home, or both) during a given day? b) If the rain probability is p = 3 /4, how many extra umbrellas does the student need to buy, so that the student stays dry with probability at least 95% (in steady-state)? c) Assume now that the student with 5 umbrellas changes his strategy, and whenever there are 5 umbrellas either at home or in the office, the student takes one regardless of whether it rains or not. What is the steady-state probability that the student gets wet? What if the student had only one umbrella, but follows the same strategy