The joint probability density function of X=[X₁,X₂,X₃]' is f(x₁,x₂,x₃)={e^(-(x₁+x₂+x₃)),0,elsewhere xⱼ > 0 j=1,2,3. Let Y=[Y₁,Y₂,Y₃]' where Y₁=X₁X₁+X₂ ; Y₂=X₁+X₂X₁+X₂+X₃ and Y₃=X₁+X₂+X₃. Find (a)

a) e^(-y₁), e^(-y₂), e^(-y₃)
b) e^(-2y₁), e^(-2y₂), e^(-2y₃)
c) e^(-3y₁), e^(-3y₂), e^(-3y₃)
d) e^(-4y₁), e^(-4y₂), e^(-4y₃)