Correlation and RegressionMCQMTP Nov 19Question 3733 of 188
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If two variables are independent their covariance is

Options

A1\displaystyle 1
B−1\displaystyle -1
C0\displaystyle 0
DNone of these
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Correct Answer

✅ Option c — 0\displaystyle 0

All Options:

  • A1\displaystyle 1
  • B−1\displaystyle -1
  • C0\displaystyle 0
  • DNone of these

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Detailed Solution & Explanation

By definition, if two random variables x\displaystyle x and y\displaystyle y are statistically independent, the expectation of their product is the product of their individual expectations:\nE(xy)=E(x)E(y)E(xy) = E(x)E(y)\n\nThe covariance between two variables x\displaystyle x and y\displaystyle y is given by the formula:\nCov(x,y)=E(xy)−E(x)E(y)Cov(x,y) = E(xy) - E(x)E(y)\n\nSubstituting the condition for independence into this formula:\nCov(x,y)=E(x)E(y)−E(x)E(y)=0Cov(x,y) = E(x)E(y) - E(x)E(y) = 0\n\nThus, the covariance of two independent variables is always 0\displaystyle 0. This corresponds to Option C.\n\nHence, **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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