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If each observation of a raw data, whose variance is σ2, is multiplied by λ, then the variance of new set is
  • a)
    σ2
  • b)
    λ2σ2
  • c)
    λ + σ2
  • d)
    λ2+ σ2
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If each observation of a raw data, whose variance is σ2, is mult...
Explanation:

Effect of Multiplying Each Observation by λ:
- When each observation of a raw data set is multiplied by a constant λ, the variance of the new set is λ^2 times the variance of the original set.

Mathematical Representation:
- Let's denote the original variance as σ^2 and the constant by λ.
- The variance of the new set, Var(λX), can be represented as Var(λX) = λ^2 Var(X).

Applying to the Given Question:
- In this question, each observation is multiplied by λ.
- Therefore, the variance of the new set is λ^2 times the original variance.
- So, the correct answer is λ^2 × σ^2, which is option 'b'.

Conclusion:
- The correct answer is option 'b', which states that the variance of the new set is λ^2 times the original variance.
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If each observation of a raw data, whose variance is σ2, is multiplied by λ, then the variance of new set isa)σ2b)λ2σ2c)λ + σ2d)λ2+ σ2Correct answer is option 'B'. Can you explain this answer?
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