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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? $\quad$
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2531 Upvotes
Verified Answer
The correct answer is:
$0.5$
$\operatorname{cov}(x, y)=30$
$$
\begin{array}{l}
\operatorname{var}(x)=25 ; \operatorname{var}(y)=144 \\
\Rightarrow r(x, y)=\frac{\operatorname{cov}(x, y)}{\sqrt{\operatorname{var}(x) \cdot \operatorname{var}(y)}} \\
\Rightarrow r(x, y)=\frac{30}{\sqrt{25 \times 144}}=\frac{30}{5 \times 12}=0.5
\end{array}
$$
$$
\begin{array}{l}
\operatorname{var}(x)=25 ; \operatorname{var}(y)=144 \\
\Rightarrow r(x, y)=\frac{\operatorname{cov}(x, y)}{\sqrt{\operatorname{var}(x) \cdot \operatorname{var}(y)}} \\
\Rightarrow r(x, y)=\frac{30}{\sqrt{25 \times 144}}=\frac{30}{5 \times 12}=0.5
\end{array}
$$
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