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Topic 9 - Joint Probability Distribution - Coggle Diagram
Topic 9 - Joint Probability Distribution
Joint Discrete 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
Joint Continuous Probability Distributions
Marginal probability density distributions :
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
