function Suppose that the random variables X and Y have joint probability density -{8 ) = f(x,y) czy if 0≤x≤ 1,0 ≤ y ≤ 1 otherwise (a) Find the value of c. (b) Find marginal probability density functions fx(x) and fy (y). (c) Find E(XY), E(X), E(Y), and cov(X,Y). (d) Are the random variables Y and V independent?

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function
Suppose that the random variables X and Y have joint probability density
cr²y if 0≤x≤ 1,0 ≤ y ≤ 1
otherwise
f(x,y) = { c₂²
(a) Find the value of c.
(b) Find marginal probability density functions fx(x) and fy(y).
(c) Find E(XY), E(X), E(Y), and cov (X, Y).
(d) Are the random variables X and Y independent?
(e) Find Pr(XY).
Transcribed Image Text:function Suppose that the random variables X and Y have joint probability density cr²y if 0≤x≤ 1,0 ≤ y ≤ 1 otherwise f(x,y) = { c₂² (a) Find the value of c. (b) Find marginal probability density functions fx(x) and fy(y). (c) Find E(XY), E(X), E(Y), and cov (X, Y). (d) Are the random variables X and Y independent? (e) Find Pr(XY).
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