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anonymous
 5 years ago
suppose X is uniform on (0,1) and Y=X. Find the joint distribution function of X and Y.
anonymous
 5 years ago
suppose X is uniform on (0,1) and Y=X. Find the joint distribution function of X and Y.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0If Y=X then the joint distribution function is \[F_{(X,Y)}(x,y)=\mathbb{P}(X\leq x,Y\leq y)=\mathbb{P}(X\leq\min(x,y))=F_X(\min(x,y))\] which in our case \[F_X(\min(x,y))=\left\{\begin{array}{ll}0&\textrm{, if }x,y\leq 0,\\x&\textrm{, if }0<x\leq y\leq 1,\\y&\textrm{, if }0<y\leq x\leq 1,\\1&\textrm{, if }1<x,y.\end{array}\right.\] The plot of the joint distribution function is attached.
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