6. Two continuous random variables X and Y have the joint density that is equal to...

6. Two continuous random variables X and Y have the joint density that is equal to c(x + y) 2 inside the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 and vanishes everywhere else.

a) Find the value of c

b) Find the marginal density f_X(x) and use it to determine E(X) and V(X)

c) Find the marginal density f_Y(y) and use it to determine E(Y) and V(Y)

d) Find the correlation ρ(X,Y)

e) Are X and Y independent? Why?

Expert Solution

orchestra answered 2 years ago

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