Download - Applied Probability Lecture 4
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Objective
Use Probability to create a software solution to a real-world problem.
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Objective
Use Probability to create a software solution to a real-world problem.
![Page 4: Applied Probability Lecture 4](https://reader035.vdocuments.us/reader035/viewer/2022062520/56815dfd550346895dcc37c8/html5/thumbnails/4.jpg)
Timeline/Administrivia
• Friday: vocabulary, Matlab• Monday: start medical segmentation project• Tuesday: complete project• Wednesday: 10am exam• Lecture: 10am-11am, Lab: 11am-12:30pm• Homework (matlab programs):
– PS 4: due 10am Monday– PS 5: due 12:30pm Tuesday
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Vocabulary
• Random variable• Discrete vs. continuous random variable• PDF• Uniform PDF• Gaussian PDF• Bayes rule / Conditional probability• Marginal Probability
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Random Variable
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Random Variable
• Function defined on the domain of an experiment
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Example r.v.
• Experiment: 2 coin tosses– Sample space: – Random variable:
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Example r.v.
• Experiment: 2 coin tosses– Sample space: HH, HT, TT, TH– Random variable: h number of heads in run
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Discrete vs. Continuous R. V.
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Discrete vs. Continuous R. V.
• Domain
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• Function that associates probability values with events in sample space.
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• Function that associates probability values with events in sample space.
• Two characteristics of a PDF:
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• Function that associates probability values with events in sample space.
• Two characteristics of a PDF:– Mean or Expected value– Variance
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Uniform PDF
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Uniform PDF
E(x) = (x) =
x
p(x)
a
?
0
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Gaussian PDF
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Gaussian PDF
2var
22
2)(
21)(
iance
mean
x
exP
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Bayes Rule Revisited)(
)()|()|(BP
APABPBAP
)P()()|()|P( ii
i xPxPx
i
PxPx )()|()P( ii
i
PxPPxPxPxPx
)()|()()|(
)P()()|()|P(
ii
ii
iii
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Recitation/Lab
• Install Matlab• Start Problem Set 1