Question Bank • QB_EM_ADV_070 MCQ • 1 Mark

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Random variables

Question Statement:

If $X$ is a random variable with variance $\operatorname{Var}(X) = 4$, then the variance $\operatorname{Var}(3 - 2X)$ is:

Options:

  • (A) $16$
  • (B) $-8$
  • (C) $12$
  • (D) $19$

Answer Key:

A

Step-by-Step Solution & Explanation

By the scaling property of variance for any constants $a$ and $b$: $\operatorname{Var}(a + bX) = b^2 \operatorname{Var}(X)$ Here $a = 3$ and $b = -2$: $\operatorname{Var}(3 - 2X) = (-2)^2 \operatorname{Var}(X) = 4 \times 4 = 16$
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