ProbabilityMCQPYQ May 23Question 3396 of 187
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If two random variables x\displaystyle x and y\displaystyle y are related by y=2−3x\displaystyle y = 2 - 3x, then the SD of y\displaystyle y is

Options

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

✅ Option a — −3×SD of x\displaystyle -3 \times \text{SD of } x

All Options:

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

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Detailed Solution & Explanation

**Poisson Distribution for Defective Bulbs** Given: - Total bulbs, n=200\displaystyle n = 200 - Probability of a defective bulb, p=0.02\displaystyle p = 0.02 - e−4=0.0183\displaystyle e^{-4} = 0.0183 Since n\displaystyle n is large and p\displaystyle p is small, we model the number of defective bulbs using the Poisson distribution with parameter λ\displaystyle \lambda: λ=np=200×0.02=4\lambda = np = 200 \times 0.02 = 4 The probability of finding exactly x\displaystyle x defective bulbs is: P(X=x)=e−λλxx!P(X = x) = \frac{e^{-\lambda} \lambda^x}{x!} For x=2\displaystyle x = 2: P(X=2)=e−4⋅422!=0.0183×162=0.0183×8=0.1464P(X = 2) = \frac{e^{-4} \cdot 4^2}{2!} = \frac{0.0183 \times 16}{2} = 0.0183 \times 8 = 0.1464 Hence, **Option A** 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.

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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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