Random variable $Y$ has moment generating function $$M_Y(t)=(0.7+0.3e^t)^4$$ Let $W=2Y-4$ what is the moment generating function of $W$?
i don't understand how $W$ interact with the $M_Y(t)$ .
2026-03-29 22:07:32.1774822052
Random variable $Y$ has moment generating function $M_Y(t)=(0.7+0.3e^t)^4 $ let $W=2Y-4$ what is the moment generating function of $W$
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Hint: $$ M_W(t) = E[e^{tW}] = E[e^{2tY - 4t}] = E[e^{2tY}e^{-4t}] = e^{-4t}E[e^{2tY}] $$