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# Review-1 - Some review problems Bayes's rule Bayes's rule A...

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Some review problems: Bayes’s rule

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Bayes’s rule box4 A kind of “reverse” conditional probability box4 Sometimes regarded as a “updating rule” for A after receiving “information” B
Example: Medical screening Tree diagram for breast cancer screening of women in twenties Cancer Incidence Cancer Diagnosis A B 0.8 “Sensitivity” False Women in 20s A c B c B B c 0.0004 0.9996 S 0.2 0.1 0.9 “Specificity” negative False positive

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Example: Medical screening (continued) Given a cancer diagnosis, what is the probability of a cancer incidence? A B B c B 0.0004 0.9996 S 0.8 0.2 0.1 A c B c 0.9
Example: Defective parts Tree diagram for parts from two different suppliers Supplier Defective A B B c 0.65 0.02 0.98 Part A c B B c 0.35 S 0.05 0.95

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A B B c B 0.65 0.35 S 0.02 0.98 0.05 Example: Defective parts (continued) Given a defective part, what is the probability it came from Supplier A? A c B c 0.95
Some review problems: Pooled Two-sample t test

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The “pooled” two-sample t statistic box4 When σ 1 = σ 2 = σ , the z-score of is box4 The “pooled” estimate of σ is n 1 + n 2 – 1 d.f.
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Review-1 - Some review problems Bayes's rule Bayes's rule A...

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