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{"ops":[{"insert":"Question 2.3 [1, 3, 3, 2, 2, 2] "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"Dr Clohessy drives to work every day, and she passes 11 traffic lights. If each traffic light works "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"independently from each other and each have a probability of being green when DR Clohessy drives "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"up to the light of 0.25. Use this information to answer the following questions. "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"a) Define the random variable X of the experiment."},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"b) What is the probability that at least two lights will be green on her morning drive through the "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"11 traffic lights? "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"c) What is the probability that at least two lights will be green, given that at least one has already "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"been green?"},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"d) What is the probability that three lights will be red through the 11 traffic lights? "},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"e) Determine the mean of X and standard deviation of X of the number of green traffic lights."},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":""},{"insert":"\n"},{"insert":"f) Now suppose you are interested in the first traffic light that turns"},{"insert":"\n"}]}
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