A ship navigating through the southern regions of the North Atlantic ice flows encounters icebergs according to

Question:

A ship navigating through the southern regions of the North Atlantic ice flows encounters icebergs according to a Poisson process. The distances between icebergs in nautical miles are exponentially distributed with a parameter λ = 0.7.
(a) What is the expected distance between iceberg encounters.'
(b) What is the probability that there is a distance of at least three nautical miles between iceberg encounters ?
(c) What is the median distance between icebergs?
(d) What is the of the number of icebergs encountered in a stretch of 10 nautical miles?
(e) What is the probability that at least five icebergs are encountered in a 10-nautical-inile stretch?
(f) What is the of the distance traveled by the ship before encountering 10 icebergs? What are the expectation and variance of this distance?
Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...