2. GOLD NUGGETS You are managing a team of miners looking for gold nuggets. If we let T be the amount of time (rounded up to whole minutes) that it takes any given miner to find a gold nugget, we assume that T is geometric with probability of success 1/240. We also assume that the time it takes different miners to find their first gold nugget are independent. Problem 2.1. Let n 2 1. Let Xn be the amount of time (rounded up to whole minutes) that it takes a team of n miners to find a first gold nugget (i.e., Xn = k if the first miner to find a gold nugget among the n miners does so after k minutes). What is Xn's distribution