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Ottawa's Confederation Line trains arrive at peak times at a stationto a station on a Poisson basis, averaging 10 trains per hour.1. What is the waiting time distribution of three trains? What is theWhat is the probability that this waiting time is at most 25 minutes? WhatWhat are the mean and variance of this random variable?2. No train arrives during the first 5 minutes of waiting. What is theWhat is the probability that there will be no train during the next 3 minutes?3. What is the probability that two trains will arrive in twelve minutes?4. At 95%, at least one train arrives in t-minutes. What is approximatelyt in minutes?5. A period of 5 minutes is said to be empty if it contains no arrivingof trains. What is the probability that at most one 5-minute periodis empty in one hour?
Question 7 A consulting engineer receives, on average, 0.7 requests per week. If the number of requests follows a Poisson process, find the probability thata) in a given week, there will be at least one request;b) in a given 4-week period, there will be at least 3 requests.
Assume that 15% of the people in your expedition tripown a mobile phone, and you are randomly assigned totwo partners in your group. Find the probability that:a) The first partner will have a mobile phone.b) The first partner will not have a mobile phone.c) That both partners will have mobile phones.d) That at most one will have a mobile phone.