STAT 462 Name ______________________________Fall 2010Exam IDirections: Answer each question below. Please be sure to show all work. Suppose the probability of correct diagnosis (either positive or negative) of steroid use is 0.90 and 2% of all professional athletes use steroids.(5 points) What is the probability a randomly chosen professional athlete will have a positive test result for steroid use? (5 points) If the athlete tests positive what is the probability s/he has actually been using steroids?(10 points) The Holiday Inn has 10 hotels in a particular city. Of these 10 hotels only 7 meet state standards for quality. A state inspector randomly chooses 4 hotels to inspect. What is the probability at least three of the inspected hotels meet the state standards for quality?Let X be a discrete random variable such that(10 points) What is (10 points) Find and (8 points) Let What is The time in minutes between the last boarding call and take-off for flights offered by an airline is a random variable X whose probability density function (pdf) is(15 points) Derive the number of minutes a traveler should expect to spend on an airplane between the last boarding call and take-off.(10 points) Find the probability a randomly selected flight takes less than the mean number of minutes to take-off after the last boarding call.Let Y be a continuous random variable with probability density function (pdf)where f and g are constants.(5 points) Suppose . What is Provide justification. (10 points) Find the constants f and g. (12 points) Find the cumulative distribution function (CDF) of Y. If you were not able to find the values of the constants in part b leave your answer in terms of f and g.1
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