If variance of is x is 5, then find the variance of (2-3x)

Option b: 45. Solution: Given: text{Var}(x) = 5 Find: text{Var}(2 - 3x) Using the property: text{Var}(a + bx) = b^2 text{Var}(x) Here a = 2, b = -3: text{Var}(2 - 3x) = (-3)^2 text{Var}(x) = 9 x 5 = 45 The given correctoption is 'a' (10), but the correct answer is 45 (Option B). Verification: 9 x 5 = 45, which is Option B. Hence, Option B is the correct answer.

Central Tendency & DispersionMTP March 21Question 3169 of 473

All Questions

If variance of is $\displaystyle x$ is $\displaystyle 5$ , then find the variance of $\displaystyle (2-3x)$

Options

\displaystyle 10

\displaystyle 45

\displaystyle 5

\displaystyle -13

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Correct Answer

✅ Option b — $\displaystyle 45$

All Options:

A $\displaystyle 10$
B $\displaystyle 45$
C $\displaystyle 5$
D $\displaystyle -13$

Detailed Solution & Explanation

**Given:**

\displaystyle \text{Var}(x) = 5

**Find:**

\displaystyle \text{Var}(2 - 3x)

**Using the property:**

\displaystyle \text{Var}(a + bx) = b^2 \cdot \text{Var}(x)

Here

\displaystyle a = 2

\displaystyle b = -3

\text{Var}(2 - 3x) = (-3)^2 \cdot \text{Var}(x) = 9 \times 5 = 45

The given `correct_option` is 'a' (10), but the correct answer is **45 (Option B)**. Verification:

\displaystyle 9 \times 5 = 45

, which is Option B. Hence, **Option B** is the correct answer.

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If variance of is x\displaystyle xx is 5\displaystyle 55, then find the variance of (2−3x)\displaystyle (2-3x)(2−3x)