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Useful Equations

Rules of Integration

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Chain Rule for Integration

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Rules of Differentiation

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Chain Rule for Differentiation

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Laws for Probabilities of Events

Venn Diagram

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Law of Addition

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Definition of Conditional Probability

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Bayes' Rule

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Random Variables (RVs)

Conditional Probability

If X and Y are discrete RVs, the definition of conditional probability for all values of y such that Pr(Y = y) > 0 is

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If X and Y are continuous RVs and have joint PDF f_XY(x,y), then the conditional PDF for all values of y such that f_Y(y) > 0 is

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For RV X, we can find Pr(X <= x) by conditioning on RV Y. If Y is a discrete RV, then

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If Y is a continuous RV with desity f_Y(y), then

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Conditional Expectation

Computing Expectations by Conditioning

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