Question: 6.17 Let (X, Y) be a random vector with joint density f(x, y) = 1 4 ) 1 + xy(x2 y2) 1 1(|x| <1,|y|

6.17 Let (X, Y) be a random vector with joint density f(x, y) = 1 4

)

1 + xy(x2 − y2)

1 1(|x|<1,|y|<1).

a) Compute the marginal distributions of X and Y.

b) Are X and Y independent?

c) Compute the characteristic functions of X and Y.

d) Compute the characteristic function of Z = X + Y.

e) What can you conclude?

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