Chapter 4 Multivariate distributions

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RS 4 Multivariate Distributions1Chapter 4Multivariate distributionsk 2Multivariate DistributionsAll the results derived for the bivariate case can be generalized to n RV. The joint CDF of X1, X2, ..., Xk will have the form: P(x1, x2, ..., xk) when the RVs are discreteF(x1, x2, ..., xk) when the RVs are continuousRS 4 Multivariate Distributions2Joint probability FunctionDefinition: joint probability FunctionLet X1, X2, ..., Xk denote k discrete random variables, then p(x1, x2, ..., xk) is joint probability function of X1, X2, ..., Xk if 112. ,,1nnxxpxx 11. 0,,1npxx 113. ,,,,nnPXXApxx 1,,nxxA Definition: joint density function Let X1, X2, ..., Xk denote k continuous random variables, then f(x1, x2, ..., xk) = n/ x1, x2, ..., xkF(x1, x2, ..., xk)is the joint density function of X1, X2.

RS – 4 – Multivariate Distributions 2 Joint Probability Function Definition: Joint Probability Function Let X1, X2, …, Xk denote k discrete random variables, then p(x1, x2, …, xk) is joint probability function of X1, X2, …, Xk if 1 2. , , 11 n n xx px x 1. 0 , , 1 px x 1 n

  Distribution, Joint, Probability, Joint probability