Motivation

History

Bayes’s Theorem

The probability that some event \(E\) occurred due to some cause \(C\) is given by Bayes’s Theorem:

\(P(E|C)=\frac{P(C|E)P(E)}{P(C)}\)

We often do not know the probability of the cause occurring in general, but we can calculate \(PC(C)\) with

\(P(C)=P(C|E)P(E)+P(C|E')P(E')\)

Worked Examples

Conclusion

Tutorial

The video tutorial summarizes this lesson.

Files & Resources

All Files for Lesson 104.151

References

None.

Errata

Let us know.

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