If two variables X and Y are independent, then what is the correlation coefficient between them?

Question

Question

This question was previously asked in

NDA (Held On: 21 Apr 2019) Maths Previous Year paper

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Answer 1

Concept

If X and Y are independent, then E(XY) = E(X)E(Y)

Covariance Cov(X, Y) of X and Y = E(XY) – E(X)E(Y)

\(Correlation~coefficient = \frac{{{\bf{Cov}}\left( {{\bf{X}},\;{\bf{Y}}} \right)}}{{{{\bf{\sigma }}_{\bf{X}}}{{\bf{\sigma }}_{\bf{Y}}}}}{\rm{\;}}\)

Calculation

Given that X and Y are independent, then the Covariance Cov(X, Y) = 0

Hence, the correlation coefficient = 0.

The correct option is (3).

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