ProbabilityMCQMTP Sep 24 Series IIQuestion 2849 of 295
All Questions

If two random variables x\displaystyle x and y\displaystyle y are related by y=−3x+8\displaystyle y = -3x + 8, then the SD of y\displaystyle y is given by

Options

A−3×SD of x\displaystyle -3 \times SD \text{ of } x
B3×SD of x\displaystyle 3 \times SD \text{ of } x
C9×SD of x\displaystyle 9 \times SD \text{ of } x
D2×SD of x\displaystyle 2 \times SD \text{ of } x
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Correct Answer

✅ Option b — 3×SD of x\displaystyle 3 \times SD \text{ of } x

All Options:

  • A−3×SD of x\displaystyle -3 \times SD \text{ of } x
  • B3×SD of x\displaystyle 3 \times SD \text{ of } x
  • C9×SD of x\displaystyle 9 \times SD \text{ of } x
  • D2×SD of x\displaystyle 2 \times SD \text{ of } x

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Detailed Solution & Explanation

For any two random variables X\displaystyle X and Y\displaystyle Y related by the linear equation Y=aX+b\displaystyle Y = aX + b (where a\displaystyle a and b\displaystyle b are constants), the relationship between their standard deviations is: SD(Y)=∣a∣×SD(X)\displaystyle \text{SD}(Y) = |a| \times \text{SD}(X). Here, the relation is y=−3x+8\displaystyle y = -3x + 8, so the coefficient a=−3\displaystyle a = -3. Thus: SD(y)=∣−3∣×SD(x)=3×SD(x)\displaystyle \text{SD}(y) = |-3| \times \text{SD}(x) = 3 \times \text{SD}(x). Hence, **Option B** is the correct answer.

About This Chapter: Probability

Paper

Paper 3: Quantitative Aptitude

Weightage

5-7 Marks

Key Topics

Probability Operations, Expected Value

A logic-heavy chapter dealing with random experiments, events (mutually exclusive, exhaustive), set theory probability, conditional probability, and Bayes' Theorem. It forms the basis for Theoretical Distributions.

View Official ICAI Syllabus

Exam Strategy Tip

Always draw a quick Venn Diagram or tree when faced with 'At least one' or 'Only A but not B' wording. It saves you from double-counting.

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