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IME 2610 Homework #2 *This assignment is due in class on 9/30. Please show work so that partial credited can be awarded.1. A. Given the CDF of random variable X, find P(X > ½). B. What is the value of asuch that P(X ≤ a) = .9 C. Determine the Probability Density Function (PDF) from the CDF. D. What type of distribution is this? 2. Having learned all about probability in your statistics class you have decided to travel to Las Vegas to compete in a poker tournament. To get to the airport you need to take a bus. There is a 30% chance that the bus will be late. If your bus is late there is a 70% chance that you will miss your flight. However, even if your bus is on time, there is still a 15% chance you will miss your flight due to traffic. Using this information answer the following questions: A. Construct a Tree Diagram for the probabilities listed above B. What is the probability that your bus is delayed but you make your flight on time? C. What is the probability that you miss your flight? D. Given that you make your flight what is the probability that your bus was delayed?