Final answer:
The variance of a random variable X that originally has variance 3 becomes 12 after multiplying X by 2, because the scale factor's square is multiplied by the original variance.
Step-by-step explanation:
When you multiply a random variable X with a variance of 3 by 2, you are scaling the random variable. To find the new variance, you must square the scale factor and multiply it by the original variance.
Therefore, the new variance of X after multiplying by 2 is 2^2 × 3, which equals 12.
To clarify with a formula, if V(X) is the variance of X, and a is the scale factor,
then the variance of the new random variable aX is V(aX) = a^2V(X).