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NDA 2018
Exam
NDA
Year
2018
Subject
Mathematics
Chapter
Statistics

NDA 2018 · Mathematics · Statistics

If the correlation coefficient between x and y is 0.6 , covariance...

If the correlation coefficient between x and y is 0.6 , covariance is 27 and variance of yy is 25 , then what is the variance of x ?

Options

  1. A95\frac{9}{5}
  2. B8125\frac{81}{25}
  3. C99
  4. D8181

Correct answer

D. 8181

Step-by-step solution

Given, r=0.6r=0.6, covariance =27,σ(y)2=25⇒σ(y)=5=27, \sigma_{(\mathrm{y})}^2=25 \Rightarrow \sigma(\mathrm{y})=5 We know, r=covariance⁡(x,y)σ(x)⋅σ(y)⇒σ(x)=covariance⁡(x,y) r. σ(y)=27(610)⋅5\mathrm{r}=\frac{\operatorname{covariance}(\mathrm{x}, \mathrm{y})}{\sigma(\mathrm{x}) \cdot \sigma(\mathrm{y})}\Rightarrow \sigma(\mathrm{x})=\frac{\operatorname{covariance}(\mathrm{x}, \mathrm{y})}{\text{ r. } \sigma(\mathrm{y})}=\frac{27}{\left(\frac{6}{10}\right) \cdot 5}=27×26=9⇒σ2(x)=81\begin{aligned} & =\frac{27 \times 2}{6}=9 \\ & \Rightarrow \sigma^2(x)=81 \end{aligned}$$
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