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I am working on a probabilty theory problem:
Let (X,Y) be distributed with joint density
f(x,y)=(1/4)(1+xy(x^2-y^2)) if abs(x)≤1, abs(y)≤1; 0 otherwise
Find the MGF of (X,Y). Are X,Y independent? If not, find covariance.
I have set up the integral to find the mgf
∫∫e^(sx+ty)f(x,y)dx dy
with both integrals from -1 to 1.
I am having trouble integrating this though in order to move on with the problem. I began to try integration by parts and I do not think that is the best route but have no other ideas.
If anyone can help, I would greatly appreciate it!
Let (X,Y) be distributed with joint density
f(x,y)=(1/4)(1+xy(x^2-y^2)) if abs(x)≤1, abs(y)≤1; 0 otherwise
Find the MGF of (X,Y). Are X,Y independent? If not, find covariance.
I have set up the integral to find the mgf
∫∫e^(sx+ty)f(x,y)dx dy
with both integrals from -1 to 1.
I am having trouble integrating this though in order to move on with the problem. I began to try integration by parts and I do not think that is the best route but have no other ideas.
If anyone can help, I would greatly appreciate it!
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