Question Bank • QB_EM_PS_001 NAT • 2 Marks

Section 1: Engineering Mathematics

Probability and Statistics

Subtopic: Mean, median, mode and standard deviation

Question Statement:

A continuous random variable $X$ has variance $\sigma^2 = 25$. The variance of the transformed random variable $Y = 3X - 15$ is ________ (answer in integer).

Answer Key:

225

Step-by-Step Solution & Explanation

From the fundamental properties of variance: $\operatorname{Var}(aX + b) = a^2 \operatorname{Var}(X)$ Here $a = 3$, $b = -15$, and $\operatorname{Var}(X) = 25$: $\operatorname{Var}(Y) = 3^2 \times 25 = 9 \times 25 = 225$
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