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Probability and Statistics ( week -9)

Probability and Statistics ( week -9). Onur DOĞAN. Chebyshev's Inequality. ( or equivalently, at least 1 - 1/ c 2  of the distribution's values are within  c  standard deviations of the mean ). Skewness. Pearson's skewness coefficients. Example.

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Probability and Statistics ( week -9)

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  1. ProbabilityandStatistics (week-9) Onur DOĞAN

  2. Chebyshev'sInequality • (or equivalently, at least 1 - 1/c2 of the distribution's values are within c standard deviations of the mean)

  3. Skewness .

  4. Pearson'sskewnesscoefficients

  5. Example • It’s been understood that, in a hosptial patients’ average hospital stay is 28, median is 25 and mode is 23 (days). • Define the skewness type, find the pearson coefficient and interpret it.

  6. SamplingDistribution .

  7. SamplingDistribution • .

  8. Central Limit Theorem • .

  9. StatisticalIntervalsfora SingleSample • .

  10. Confidence Interval on the Mean of a Normal Distribution,VarianceKnown • .

  11. Confidencelntervals .

  12. Confidencelntervals .

  13. Example • .

  14. Solution .

  15. Confidence Interval on the Mean of a Normal Distribution,VarianceUnknown(t distribution) .

  16. A Large-SampleConfidenceIntervalfor a PopulationProportion • Confidence Interval Formula: • Sample Size Selection

  17. Example .

  18. Solution .

  19. SummaryforConfidenceIntervals • .

  20. Examples

  21. Example • .

  22. Solution

  23. Example • .

  24. Solution • .

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