Given Y = 3 − 2X, E[X] = 5, and Var(X) = 4, which statement is correct?

Given the linear transformation $Y = aX + b$, the expected value is $E[Y] = aE[X] + b$.
In this case, $Y = 3 - 2X$, so $a = -2$ and $b = 3$.
We are given $E[X] = 5$.

$$E[Y] = E[3 - 2X] = 3 - 2E[X]$$ $$E[Y] = 3 - 2(5)$$ $$E[Y] = 3 - 10$$ $$E[Y] = -7$$

Given the linear transformation $Y = aX + b$, the variance is $Var(Y) = a^2 Var(X)$.
In this case, $Y = 3 - 2X$, so $a = -2$.
We are given $Var(X) = 4$.

$$Var(Y) = Var(3 - 2X) = (-2)^2 Var(X)$$ $$Var(Y) = (4)(4)$$ $$Var(Y) = 16$$

Our calculations show $E[Y] = -7$ and $Var(Y) = 16$.
Option D states: $E[Y] = 3 - 2E[X] = -7$ and $Var(Y) = (-2)^2 Var(X) = 16$. This matches our results.

The correct statement is D.

$$\boxed{\text{D. } E[Y] = 3 - 2E[X] = -7 \text{ and } Var(Y) = (-2)^2 Var(X) = 16}$$