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GATE 2021 EC – Question 13

Engineering Mathematics · Probability and Statistics · 1 mark · Multiple choice

Two continuous random variables $X$ and $Y$ are related as

$$Y=2X+3$$

Let $\sigma_X^2$ and $\sigma_Y^2$ denote the variances of $X$ and $Y$, respectively. The variances are related as

  1. $\sigma_Y^2=2\sigma_X^2$
  2. $\sigma_Y^2=4\sigma_X^2$
  3. $\sigma_Y^2=5\sigma_X^2$
  4. $\sigma_Y^2=25\sigma_X^2$

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Show answer and explanation

Correct answer: (B) $\sigma_Y^2=4\sigma_X^2$

Explanation

Adding a constant does not change the variance, and scaling by 2 multiplies it by $2^2$. So $\sigma_Y^2=4\sigma_X^2$.