MGF Method

Method

MGF uniquely characterizes the distribution of a RV. For RV $X,Y$ with MGF $m_X(t),m_Y(t)$

$$m_X(t)=m_Y(t)⟺X\sim Y$$

Intuition

If $m_Y(t)$ follows the MGF of some known distribution $⟹$ $Y$ follows that distribution