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UNFORMATTED ATTACHMENT PREVIEW
PRE-REQUISITE TESTS •1. Use the Gaussian Elimination method to solve: • 1x + 2y + 3z = 10 • 2x + 1y + 3z = 11 • 2x + 3y + 1z = 13 • 2. The relative frequency distribution of the number of TVs sold in a day in a department store in the last year is as follows: • Number of TV sold 0 1 2 3 4 • Relative Frequency (probability) 0.2 0.4 0.25 0.1 0.05 • Compute the mean and standard deviation of this distribution. • 3. Human IQ scores are approximately normally distributed with mean 100 and standard deviation 15. Determine the minimum IQ scores for the top 10% of the population. • 4. Initial diagnosis of a patient’s illness was potentially flu (F), cold (C), or hay fever (H), with probabilities 0.1, 0.3, and 0.6 respectively. A lab test was then taken from the patient. Past tests on similar patients show the following conditional probabilities on the test result being positive (+), neutral (0), or negative (-): • P(+|F) = 0.6 P(0|F) = 0.3 P(-|F) = 0.1 • P(+|C) = 0.1 P(0|C) = 0.7 P(-|C) = 0.2 • P(+|H) = 0.1 P(0|H) = 0.1 P(-|H) = 0.8 •Use the Bayes Theorem to estimate the respective probabilities of F, C, and H given that a +, 0, or – test result has been observed.
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