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Unformatted text preview: 09/10 p. 1 THE UNIVERSITY OF HONG KONG DEPARTMENT OF STATISTICS AND ACTUARIAL SCIENCE STAT1301 Probability and Statistics I Class Test Solution October 30, 2009 1. [10 marks] (a) State the definition of random variable . Ans: A random variable ℜ → Ω : X is a numerical valued function defined on a sample space. In other words, a number ( ) ω X , providing a measure of the characteristic of interest, is assigned to each outcome ω in the sample space. (b) Without using any mathematical expression, describe the memoryless property verbally. Ans: A nonnegative random variable has the memoryless property if when it is used to model the time of occurrence of an event, the fact that it hasn't happened yet, tells us nothing about how much longer it will take before it does happen, i.e. “the future is independent of the past”. P. T. O. 09/10 p. 2 2. [10 marks] A HIV test has a sensitivity of 99.7% and a specificity of 98.5%. Suppose that a subject, from a population with a 0.1% prevalence of HIV, receives a positive test result. What is the from a population with a 0....
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