I don't understand how to calculate the linear combination to find Y from X. Any help is appreciated. Thanks.
Suppose $Y = (3X − 2)^2$, and $E[X] = 2$, $var(X) = 5$. Find $E[Y ]$.
2026-03-25 04:39:40.1774413580
A linear combination of the E[X] of random variable X
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The Comments of @HarryAlli and @copper.hat give very good clues.
I will show key clues for working a similar problem: finding $E(V),$ where $V = (3X + 1)^2.$
$$E(V) = E[(3X + 1)^2] = \cdots = 9E(X^2) + 6E(X) + 1.$$ You know $E(X)$ and need $E(X^2).$ For that, consider $$ 5 = Var(X) = E(X^2) - [E(X)]^2 = E(X^2) - 4.$$
Something similar works for your problem.