If 2x + 3y = 0 and v(x) = 6 then v(y) is:

Option a: 8/3. Solution: Given: 2x + 3y = 0, V(x) = 6 Step 1: Express y in terms of x. 3y = -2x y = -2/3x Step 2: Apply variance property. V(y) = V<=ft(-2/3xright) = <=ft(-2/3right)^2 V(x) = 4/9 x 6 = 24/9 = 8/3 Hence, Option A is the correct answer.

Central Tendency & DispersionMTP Dec 22 - Series IQuestion 3192 of 473

All Questions

If $\displaystyle 2x + 3y = 0$ and $\displaystyle v(x) = 6$ then $\displaystyle v(y)$ is:

Options

\displaystyle \frac{8}{3}

C-9

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Correct Answer

✅ Option a — $\displaystyle \frac{8}{3}$

All Options:

A $\displaystyle \frac{8}{3}$
B9
C-9
D6

Detailed Solution & Explanation

**Given:**

\displaystyle 2x + 3y = 0

\displaystyle V(x) = 6

**Step 1: Express

\displaystyle y

in terms of

\displaystyle x

.**

3y = -2x

y = -\frac{2}{3}x

**Step 2: Apply variance property.**

V(y) = V\left(-\frac{2}{3}x\right) = \left(-\frac{2}{3}\right)^2 \cdot V(x) = \frac{4}{9} \times 6 = \frac{24}{9} = \frac{8}{3}

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

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If 2x+3y=0\displaystyle 2x + 3y = 02x+3y=0 and v(x)=6\displaystyle v(x) = 6v(x)=6 then v(y)\displaystyle v(y)v(y) is: