Suppose the random vector (X,Y) is uniformly distributed on the interior of the triangle with vertices at (1,1),(-1,1), and (0,-2). (Note that the area of this triangle is three.) a. Find and...

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Suppose the random vector (X,Y) is uniformly distributed on the interior of the triangle with<br>vertices at (1,1),(-1,1), and (0,-2). (Note that the area of this triangle is three.)<br>a. Find and carefully sketch the graph of the pdf of X.<br>b. Find and carefully sketch the graph of the pdf of Y.<br>c. Find E(Y|X=x).<br>d. Find E(X|Y=y).<br>e. Find Var(Y|X=x).<br>f. Find Var(X|Y=Dy).<br>

Extracted text: Suppose the random vector (X,Y) is uniformly distributed on the interior of the triangle with vertices at (1,1),(-1,1), and (0,-2). (Note that the area of this triangle is three.) a. Find and carefully sketch the graph of the pdf of X. b. Find and carefully sketch the graph of the pdf of Y. c. Find E(Y|X=x). d. Find E(X|Y=y). e. Find Var(Y|X=x). f. Find Var(X|Y=Dy).

Jun 10, 2022

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Suppose the random vector (X,Y) is uniformly distributed on the interior of the triangle with vertices at (1,1),(-1,1), and (0,-2). (Note that the area of this triangle is three.) a. Find and...

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