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Unformatted text preview: Practice Final 1 1. A screening test for a disease shows a positive test result in 95% of all cases when the disease is actually present and in 10% of all cases when it is not. If the prevalence of the disease is 1 in 50, and an individual tests positive, what is the probability that the individual actually has the disease? 2 2. Let X be a random variable with distribution function F ( x ) = x < . 1 0 ≤ x < 1 . 3 . 3 1 . 3 ≤ x < 1 . 7 . 8 1 . 7 ≤ x < 1 . 9 . 9 1 . 9 ≤ x < 2 1 x ≥ 2 Determine the probability mass function of X . 3 3. Let X and Y be two random variables with joint distribution X = 0 X = 1 Y=0 0.2 0.3 Y=1 0.0 0.5 (a) Find P ( X = 1 ,Y = 0). (b) Find P ( X = 1). (c) Find E ( X ). (d) Find var( Y ). (e) Find E ( XY ). 4 4. A TRUEFALSE exam has 20 questions. Find the expected number of correct answers if a student guesses the answer at random....
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 Winter '07
 SCHONMANN
 Standard Deviation, Variance, Probability theory, Probability mass function, positive test result

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