If variance of 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 x 5 = 9 x 5 = 45 Hence, Option B is the correct answer.

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

The correct answer is Option b: $45$. **Given:** $\text{Var}(x) = 5$ **Find:** $\text{Var}(2 - 3x)$ **Using the property:** $\text{Var}(a + bx) = b^2 \cdot \text{Var}(x)$ Here $a = 2$, $b = -3$: $$\text{Var}(2 - 3x) = (-3)^2 \times 5 = 9 \times 5 = 45$$ Hence, **Option B** is the correct answer.

Central Tendency & DispersionMTP June 24 Series IQuestion 3207 of 473

All Questions

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

Options

\displaystyle 10

\displaystyle 45

\displaystyle 3

\displaystyle 13

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Correct Answer

✅ Option b — $\displaystyle 45$

All Options:

A $\displaystyle 10$
B $\displaystyle 45$
C $\displaystyle 3$
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 \times 5 = 9 \times 5 = 45

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

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