If the variance of random variable 'x' is 17, then what is variance of y = 2x+5?

Option c: 68. Solution: Given: text{Var}(x) = 17 Find: text{Var}(y) where y = 2x + 5 Key Property of Variance: For a linear transformation y = a + bx: text{Var}(y) = b^2 text{Var}(x) The additive constant a does NOT affect variance. Step 1: Identify b = 2 (the multiplier of x). Step 2: Apply the formula. text{Var}(2x + 5) = (2)^2 text{Var}(x) = 4 x 17 = 68 Hence, Option C is the correct answer.

If the variance of random variable '$x$' is 17, then what is variance of $y = 2x+5$?

The correct answer is Option c: $68$. **Given:** $\text{Var}(x) = 17$ **Find:** $\text{Var}(y)$ where $y = 2x + 5$ **Key Property of Variance:** For a linear transformation $y = a + bx$: $$\text{Var}(y) = b^2 \cdot \text{Var}(x)$$ The additive constant $a$ does NOT affect variance. **Step 1:** Identify $b = 2$ (the multiplier of $x$). **Step 2:** Apply the formula. $$\text{Var}(2x + 5) = (2)^2 \cdot \text{Var}(x) = 4 \times 17 = 68$$ Hence, **Option C** is the correct answer.

Central Tendency & DispersionPYQ Dec 22Question 3139 of 473

All Questions

If the variance of random variable ' $\displaystyle x$ ' is 17, then what is variance of $\displaystyle y = 2x+5$ ?

Options

\displaystyle 34

\displaystyle 39

\displaystyle 68

\displaystyle 78

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Correct Answer

✅ Option c — $\displaystyle 68$

All Options:

A $\displaystyle 34$
B $\displaystyle 39$
C $\displaystyle 68$
D $\displaystyle 78$

Detailed Solution & Explanation

**Given:**

\displaystyle \text{Var}(x) = 17

**Find:**

\displaystyle \text{Var}(y)

where

\displaystyle y = 2x + 5

**Key Property of Variance:** For a linear transformation

\displaystyle y = a + bx

\text{Var}(y) = b^2 \cdot \text{Var}(x)

The additive constant

\displaystyle a

does NOT affect variance. **Step 1:** Identify

\displaystyle b = 2

(the multiplier of

\displaystyle x

). **Step 2:** Apply the formula.

\text{Var}(2x + 5) = (2)^2 \cdot \text{Var}(x) = 4 \times 17 = 68

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

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If the variance of random variable 'x\displaystyle xx' is 17, then what is variance of y=2x+5\displaystyle y = 2x+5y=2x+5?