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In a reality show, two judges independently provided marks base do the performance of the participants. If the marks provided by the second judge are given by Y = 10.5 + 2x, where X is the marks provided by the first judge. If the variance of the marks provided by the second judge is 100, then the variance of the marks provided by the first judge is:




Solution

Statistics Puzzle: Variance under Linear Transformation

Given:

  • Y = 10.5 + 2X
  • Var(Y) = 100

Formula: If Y = a + bX, then Var(Y) = b² × Var(X)

Apply:

  • 100 = 2² × Var(X)
  • 100 = 4 × Var(X)
  • Var(X) = 100 / 4 = 25

✅ Final Answer: The variance of the marks given by the first judge is 25.


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