Two dice are thrown. Their respective random outcomes are (X_{1}) and (X_{2}). Let (X=max left(X_{1}, X_{2} ight))
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Two dice are thrown. Their respective random outcomes are \(X_{1}\) and \(X_{2}\). Let \(X=\max \left(X_{1}, X_{2}\right)\) and \(Y\) be the number of even components of \(\left(X_{1}, X_{2}\right) . X\) and \(Y\) have the respective ranges \(R_{X}=\{1,2,3,4,5,6\}\) and \(R_{Y}=\{0,1,2\}\).
(1) Determine the joint probability distribution of the random vector \((X, Y)\) and the corresponding marginal distributions. Are \(X\) and \(Y\) independent?
(2) Determine \(E(X), E(Y)\), and \(E(X Y)\).
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Related Book For
Applied Probability And Stochastic Processes
ISBN: 9780367658496
2nd Edition
Authors: Frank Beichelt
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