Let A denote the set of all points (x, y) in the two-dimensional plane that satisfy the con strai...

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Let A denote the set of all points (x, y) in the two-dimensional plane that satisfy the con straints: (a) 2 + y2 < 2, and (b)

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Answer 1

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The joint PDF is, $f_{X,Y}\left ( x,y \right )=\frac{1}{\pi };x^2+y^2\leqslant 2,x\geqslant 0$ . The region is a semicircle circle with radius $\sqrt{2}$ .

a)The marginal PDF of $X$ . Dependent of $X$ , $Y$ varies from $-\sqrt{2-X^2}$ to $2-X2$

$V2-x2 fx,y (x, V) dy V2-x2 fy (x) = ду fy(x) =$

b)The marginal PDF of $Y$ . Dependent of $Y$ , $X$ varies from 0 to $\sqrt{2-Y^2}$

$ћу (x, y) dy 0 fy (Y) = dy 0 fr (Y)-$

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Answer 2

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Let A denote the set of all points (x, y) in the two-dimensional plane that satisfy the con strai...

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