If the joint probability density of X and Y is given by f(x,y) = {2 for x > 0, y > 0, x + y < 1 {0 else, then find P(X + Y > 2/3) and P(X > 2Y). I used an integral formula to find F(x,y) = 1/2. Is this applicable in any way? Much appreciated
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Originally Posted by noles2188 If the joint probability density of X and Y is given by f(x,y) = {2 for x > 0, y > 0, x + y < 1 {0 else, then find P(X + Y > 2/3) and P(X > 2Y). I used an integral formula to find F(x,y) = 1/2. Is this applicable in any way? Much appreciated Did you draw the diagrams? P(X + Y > 2/3) can be found using simple geometry. I get . P(X > 2Y) can be found using simple geometry. I get where h is the y-coordinate of the intersection point of y = x/2 and y = 1 - x.
what do you mean by "F(x,y) = 1/2"?
Originally Posted by matheagle what do you mean by "F(x,y) = 1/2"? That was a misprint on my part. F(x, y) = 1/2 when P(X<= 1/2, Y<= 1/2)
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