- #1
cjaylee
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Let the joint PDF of (X,Y) be of the form:
f(x,y) = 1/8x(x-y), 0<=x<=2, |y|<=x
f(x,y) = 0 elsewhere
Find P(X+Y<=2).
The answer that my teacher gave was
P(X+Y<=2)=∫01dx ∫-xx 1/8x(x-y)dy + ∫12dx ∫-x2-x 1/8x(x-y)dy
I do not understand how my teacher could separate the integral like that ∫ dx ∫ dy when the function has both the variable x and y. Shouldn't that be only possible when we can separate the function into 2 separate functions that are independent of each other?
Thanks for the help!
f(x,y) = 1/8x(x-y), 0<=x<=2, |y|<=x
f(x,y) = 0 elsewhere
Find P(X+Y<=2).
The answer that my teacher gave was
P(X+Y<=2)=∫01dx ∫-xx 1/8x(x-y)dy + ∫12dx ∫-x2-x 1/8x(x-y)dy
I do not understand how my teacher could separate the integral like that ∫ dx ∫ dy when the function has both the variable x and y. Shouldn't that be only possible when we can separate the function into 2 separate functions that are independent of each other?
Thanks for the help!