Find the constants c₁ and c₂ such that the quantity W(X) =E(X³) +c₁ E(X)E(X²) +c₂[E(X)]³ satisfies the property W(X₁+X₂) =W(X₁) +W(X₂) for any bounded and independent random variables X₁ and X₂.

Hint.One can either work with this expression directly, or usethe equality X₁+X₂(t) =X₁(t) +X₂(t), where X(t) = ln(E(e^tx)).