Topic 9 - Joint Probability Distribution

Joint Discrete Probability Distributions

Joint Continuous Probability Distributions

Joint discrete distributions:


P(( X , Y ) ∈ A )) = ∑( x , y ) ∑∈ A p( x , y )

Marginal probability mass distributions:


P( x ) = Σy p( x , y ) , P(y) = Σx p( x , y )

Expected values for
discrete random variables

Expected value of X, E( X ) = μx

Expected value of Y, E( Y ) = μy

Expected variances for
discrete random variables

Variance of X, Var( X ) = σ^2x

Variance of Y, Var( Y ) = σ^2y

Covariance for discrete random variables :


cov( X , Y ) = Variance of X, Var( X ) = σxy

Correlation for discrete random variables : ρ = σxy / σx * σy

Marginal probability density distributions : Screenshot (66) Screenshot (66)


Expected values for
continuous random variables

Expected value of X, E( X ) = μx

Expected value of Y, E( Y ) = μy

Variances for
continuous random variables

Variance of X, Var( X ) = σ^2x

Variance of Y, Var( Y ) = σ^2y

Covariance for continuous random variables :


cov( X , Y ) = σxy

Correlation for continuous random variables :
ρ = σxy / σx * σy