8. A pair of jointly continuous random variables, X and Y have the joint density 10 function uniform distributed over 1/2

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8. A pair of jointly continuous random variables, X and Y have the joint density 10
function uniform distributed over 1/2<x+y<1, if 0 < x, y ≤1 and 0 elsewhere.
(a) Find the PDF, fxy(x, y).
(b) Find the marginal PDFs of X and Y, i.e. fx (x) and fy (y).
(c) Find E[XY ] and Var[X]
(d) Find the conditional PDF for X given that Y3/4, i.e., Jxy (2|3/4).
Transcribed Image Text:8. A pair of jointly continuous random variables, X and Y have the joint density 10 function uniform distributed over 1/2<x+y<1, if 0 < x, y ≤1 and 0 elsewhere. (a) Find the PDF, fxy(x, y). (b) Find the marginal PDFs of X and Y, i.e. fx (x) and fy (y). (c) Find E[XY ] and Var[X] (d) Find the conditional PDF for X given that Y3/4, i.e., Jxy (2|3/4).
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