For the exponential distribution, you can use: "rexp(n,lambda)" to sample n wait times that follow an exp(A) distribution. "pexp(x,A)" to find P(X < | X 2 exp(A)) "qexp(q, A)" to find the wait time value corresponding to the qth quantile of exp(A). The intervals between potholes in a road (in meters) can be modeled as an exponential distribution. You are on a stretch of road that averages 1 pothole every 90 meters. Use R methods to answer the following questions. Report ALL decimal places. a. What is the probability that the next pothole will be within the next 10 meters? b. What is the probability that you'll drive more than 100 meters without any potholes? c. What is the probability that the next pothole will be between 30 and 40 meters away from your current position? d. There's a 95% chance that the next pothole will be within meters. e. The median distance you'd travel to the next pothole is meters. f. Using the random seed of 12, simulate a reasonable value for the distance between the your position and the first pothole: