Problem 4 (3 points) A car rental has n cars parked in a row, call them C1,,Cn. For any given customer, the probability that they want to rent the car Ci is pi(0,1). After entering the parking lot, the customer has to pass the cars from left to right until they arrive at the car they have chosen to rent. For a given permutation of {1,,n} such that the cars are put in the order (C(1),,C(n)) from left to right, let T be the number of cars a costumer has to pass before they reach their required car. Find the specific permutation such that the probability P{Tk} is minimal for all k= 1,,n, i.e. find such that minmink=1,n(P{Tk}P{Tk})0 It is enough to give a heuristic answer. Hint: Try to build an intuition using concrete values for n and p1,,pn. For example, let n=4 and p1=102,p2=101,p3=104, and p4=103. In which order would you put the cars so as to minimize the probabilities that a costumer has to pass k cars (k=0,1,2,3) ? Problem 4 (3 points) A car rental has n cars parked in a row, call them C1,,Cn. For any given customer, the probability that they want to rent the car Ci is pi(0,1). After entering the parking lot, the customer has to pass the cars from left to right until they arrive at the car they have chosen to rent. For a given permutation of {1,,n} such that the cars are put in the order (C(1),,C(n)) from left to right, let T be the number of cars a costumer has to pass before they reach their required car. Find the specific permutation such that the probability P{Tk} is minimal for all k= 1,,n, i.e. find such that minmink=1,n(P{Tk}P{Tk})0 It is enough to give a heuristic answer. Hint: Try to build an intuition using concrete values for n and p1,,pn. For example, let n=4 and p1=102,p2=101,p3=104, and p4=103. In which order would you put the cars so as to minimize the probabilities that a costumer has to pass k cars (k=0,1,2,3)