In: Statistics and Probability
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 fX(x) and use it to determine E(X) and V(X)
c) Find the marginal density fY(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?