EE 605 Problem 1 a. b. Problem 2 Problem 3 Problem 4 Problem 5 Intro to Probability & Stochastic Processes I HOMEWORK 3 Trains X and Y arrive at a station at random times between 8:00 a.m. and 8:20 a.m. Train X stops at the station for 3 minutes and Train Y stops for 5 minutes. Trains arrive at times that are independent of each other. Find the probability that Train X arrives before train Y. Trains meet at the station. A 40-year-old woman without any symptoms or family history of breast cancer has a mammogram as part of a routine checkup. A week later she receives a letter saying her test result was abnormal. She needs additional testing. Using Bayes's theorem, find the probability that the woman actually has breast cancer. Here are some statistical data about that low-risk group of women, aged 40 to 50, which you will need for calculation: The probability that one of these women has breast cancer is 0.8%. If a woman has breast cancer, the probability is 90% that she will have a positive mammogram. If a woman does not have breast cancer, the probability is 7% that she will