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NDA 2016
Exam
NDA
Year
2016
Subject
Mathematics
Chapter
Statistics

NDA 2016 · Mathematics · Statistics

If the covariance between x and y is 30 , variance of x is 25 and...

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?

Options

  1. A0.40.4
  2. B0.50.5
  3. C0.60.6
  4. D0.70.7

Correct answer

B. 0.50.5

Step-by-step solution

cov⁡(x,y)=30var⁡(x)=25;var⁡(y)=144⇒r(x,y)=cov⁡(x,y)var⁡(x)⋅var⁡(y)⇒r(x,y)=3025×144=305×12=0.5\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}
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