When r = 0 then cov(x,y) is equal to

Option c: 0. Solution: Relationship between r and (x,y) : Formula: r = (x,y) × If r = 0 , then: 0 = (x,y) × Since ≠ 0 and ≠ 0 (assuming non-degenerate distributions): (x,y) = 0 Note: The given correctoption says 'a' (+1), but this is incorrect. When r = 0 , (x,y) = 0 by the definition of r . Hence, Option C is the correct answer.

When $r = 0$ then $cov(x,y)$ is equal to

The correct answer is Option c: $0$. **Relationship between $r$ and $\\text{Cov}(x,y)$:** Formula: $$r = \\frac{\\text{Cov}(x,y)}{\\sigma_x \\cdot \\sigma_y}$$ If $r = 0$, then: $$0 = \\frac{\\text{Cov}(x,y)}{\\sigma_x \\cdot \\sigma_y}$$ Since $\\sigma_x \\neq 0$ and $\\sigma_y \\neq 0$ (assuming non-degenerate distributions): $$\\text{Cov}(x,y) = 0$$ Note: The given `correct_option` says 'a' (+1), but this is incorrect. When $r = 0$, $\\text{Cov}(x,y) = 0$ by the definition of $r$. Hence, **Option C** is the correct answer.

Correlation and RegressionMCQMTP Nov 20Question 3652 of 188

All Questions

When $\displaystyle r = 0$ then $\displaystyle cov(x,y)$ is equal to

Options

\displaystyle +1

\displaystyle -1

\displaystyle 0

DNone

For any discrepancies in this question, email contact@cadada.in

Correct Answer

✅ Option c — $\displaystyle 0$

All Options:

A $\displaystyle +1$
B $\displaystyle -1$
C $\displaystyle 0$
DNone

Detailed Solution & Explanation

**Relationship between

\displaystyle r

and

\displaystyle \\text{Cov}(x,y)

:** Formula:

r = \\frac{\\text{Cov}(x,y)}{\\sigma_x \\cdot \\sigma_y}

\displaystyle r = 0

, then:

0 = \\frac{\\text{Cov}(x,y)}{\\sigma_x \\cdot \\sigma_y}

Since

\displaystyle \\sigma_x \\neq 0

and

\displaystyle \\sigma_y \\neq 0

(assuming non-degenerate distributions):

\\text{Cov}(x,y) = 0

Note: The given `correct_option` says 'a' (+1), but this is incorrect. When

\displaystyle r = 0

\displaystyle \\text{Cov}(x,y) = 0

by the definition of

\displaystyle r

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

About This Chapter: Correlation and Regression

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Correlation Coefficient, Regression Equations

This chapter covers Correlation Coefficient, Regression Equations and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

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Correlation vs Regression: Statistics for CA Foundation

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When r=0\displaystyle r = 0r=0 then cov(x,y)\displaystyle cov(x,y)cov(x,y) is equal to