Central Tendency & DispersionMTP June 2023 Series IQuestion 3197 of 473
All Questions

If the variance of random variable 'x\displaystyle x' is 18\displaystyle 18, then what is variance of y=2x+5\displaystyle y = 2x + 5?

Options

A34\displaystyle 34
B39\displaystyle 39
C68\displaystyle 68
D72\displaystyle 72
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Correct Answer

✅ Option d — 72\displaystyle 72

All Options:

  • A34\displaystyle 34
  • B39\displaystyle 39
  • C68\displaystyle 68
  • D72\displaystyle 72

Detailed Solution & Explanation

**Given:** Var(x)=18\displaystyle \text{Var}(x) = 18 **Find:** Var(y)\displaystyle \text{Var}(y) where y=2x+5\displaystyle y = 2x + 5 **Using the property:** Var(a+bx)=b2⋅Var(x)\displaystyle \text{Var}(a + bx) = b^2 \cdot \text{Var}(x) Here a=5\displaystyle a = 5, b=2\displaystyle b = 2: Var(2x+5)=(2)2×18=4×18=72\text{Var}(2x + 5) = (2)^2 \times 18 = 4 \times 18 = 72 So Var(y)=72\displaystyle \text{Var}(y) = 72 (Option D). The given `correct_option` 'b' (39) is incorrect. Hence, **Option D** is the correct answer.

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