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math80.sample quiz11 - latest edit Tuesday:12 pm wostner...

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latest edit: Tuesday, March 24, 01:12 pm wostner : probability : benford distribution exercises ©2006-2009 ulf wostner<[email protected]> benford distribution Definition: A random variable X with DOMAIN = {1, 2, 3, 4, 5 ,6 ,7 , 8, 9} and probability function p(d) = log( (d+1) ⁄ d) is said to have Benford Distribution , and we will write X = BENFORD exercises 1. Using your calculator, calculate all the probabilities p(d) and enter them into the p(d) column below. d p(d) d p(d) d 2 p(d) 1 0.3010 2 3 4 5 6 7 8 9 1.0000 2. Answer: For example, p(9) = 0.0458. Verify that Σp(d)=1 3. Calculate both E(X) and SD(X) . Use our usual shortcut formulas for E(X) and SD(X), and show your calculations in the table above. Answer: E(X) = 3.4402, SD(X) = 2.4610
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4. Create a table showing the cumulative frequencies for p(d), completing the table below. d p(d) cum(d) 1-cum(d) 1 0.3010 2 3 0.6021 4 5 6 7 8 9 1.0000 1.0000 5. Use your table above to calculate P(X ≥ 5). Answer: … 6. Use your table above to calculate P(X < 5). Answer: … 7.
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