Assume that the joint density function of random variables X and Y is given by f_xy(x,y)=...

 

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Assume that the joint density function of random variables X and Y is given by f_xy(x,y)= (3/5)(1+x^2+y^2) 0<x<1, 0<y<1 0, elsewhere a) Find the marginal density functions of X and Y b) Are the random variables X and Y independent? Justify your answer! c) Find the conditional density functions f_x/y(x/y) and f_y/x(y/x) d) Find P(X</Y<¾) e) Find P(X</Y=¹/2) f) Find P(X=1 /Y<½) Assume that the joint density function of random variables X and Y is given by f_xy(x,y)= (3/5)(1+x^2+y^2) 0<x<1, 0<y<1 0, elsewhere a) Find the marginal density functions of X and Y b) Are the random variables X and Y independent? Justify your answer! c) Find the conditional density functions f_x/y(x/y) and f_y/x(y/x) d) Find P(X</Y<¾) e) Find P(X</Y=¹/2) f) Find P(X=1 /Y<½)

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SOLUTION a To find the marginal density function of X we need to integrate the joint density function over all possible values of Y fxx fxyxydy 351x2y2dy from y0 to y1 35y yx2 13y3 from y0 to y1 351 x... View the full answer