Question: A point is uniformly distributed in a triangle, ABC as illustrated in the diagram, we use a two dimensional random variable (X,Y) to denote position

A point is uniformly distributed in a triangle, ABC as illustrated in the diagram, we use a two dimensional random variable (X,Y) to denote position of the point. Now we are interested in the deviation between X and Y, denoted as Z= |X-Y|

Find the CDF of Z

Find the PDF of Z

Find the expectation of Z

Are X and Y independent? Justify your answer.

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