I would like a detailed explanation for the following continuous random variable exercise.

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 proper 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 first 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?