Topic 9
Joint Probability Distribution

Joint discrete distribution is also called joint probability mass function (joint pmf)

Definition

Marginal Probability Mass Distributions

𝑝(𝑥, 𝑦) = 𝑃(𝑋 = 𝑥 𝑎𝑛𝑑 𝑌 = 𝑦)

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Type of variable

mass function for discrete rv

density function for continuous rv

Expected Values for Discrete RV

Expected value of X, E(X)

Variances for Discrete RV

Variance of X, Var(X)

Covariance for Discrete RV

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Correlation Coefficient

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Marginal Probability Density Distributions

Expected Values Continuous RV

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Expected value of X, E(X)

Variances Continuous RV

Variance of X, Var(X)

Covariance for Continuous RV

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Correlation Coefficient

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Expected value of Y, E(Y)

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Variance of Y, Var(Y)

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Expected value of Y, E(Y)

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Variance of Y, Var(Y)

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