Q267 / 270 · NDA 2016 (Phase 2) · Mathematics

If the covariance between x and y is 30 , variance of x is 25 and variance of y is 144 , then what is the correlation coefficient?

  • A
    $0.4$
  • Correct answer
    B
    $0.5$
  • C
    $0.6$
  • D
    $0.7$

Solution

$\begin{aligned} & \operatorname{cov}(x, y)=30 \\ & \operatorname{var}(x)=25 ; \operatorname{var}(y)=144 \\ & \Rightarrow r(x, y)=\frac{\operatorname{cov}(x, y)}{\sqrt{\operatorname{var}(x) \cdot \operatorname{var}(y)}} \\ & \Rightarrow r(x, y)=\frac{30}{\sqrt{25 \times 144}}=\frac{30}{5 \times 12}=0.5\end{aligned}$

Hence, the correct answer is option: 'B'.

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