I'd like a tutor to answer these, thanks.

4-. Suppose the time {in minutes] it takes for a taxi to arrive at a customer once dispatched by base has the following distribution: | h EsCy-th fivl = [1 off" runs! a] What distribution is this? Name the distribution and clearly write the distribution function including the support of the function. Correct answers must incl ude the pro per notation. b] if EUII} = E: Farm], find the value of d. c} Suppose a taxi is dispatched by base, what is the probability that it takes more than 1.5 minutes to get to the customer? d} Forty percent of the taxis dispatched by base, arrive at the customer in what time or less? 5. The mean rate for the number of potholes per kilometre on the Dunrobin Road to Mandela Highway stretch is 1.6. a] What distribution is this? Name the distribution and clearly write the distribution function including the support of the function. Correct answers must include the pro per notation. b] Suppose you are interested in the probability that you go for more than 0.5km before you get to the first pothole. i. What type of distribution is this? Name the distribution and clearly write the distribution function include the support of the function. Correct answers must include the proper notation. ii. Show that the average distance between potholes is 0.625km {you must prove this from rst principles} iii. What is the median distance between potholes? iv. Given your answers above, what does this tell you about the shape of the distribution