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Let the correlation coefficient between $\mathrm{X}$ and $\mathrm{Y}$ be $0.6$. Random variables $\mathrm{Z}$ and $\mathrm{W}$ are defined as $\mathrm{Z}=\mathrm{X}+5$ and $\mathrm{W}$
$=\frac{Y}{3}$. What is the correlation coefficient between $\mathrm{Z}$ and $\mathrm{W}$ ?
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$=\frac{Y}{3}$. What is the correlation coefficient between $\mathrm{Z}$ and $\mathrm{W}$ ?
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The correct answer is:
$0.6$
Given, $\mathrm{r}_{x y}=0.6$
$\mathrm{z}=\mathrm{x}+5 ; w=\frac{y}{3}$
$\Rightarrow \mathrm{b}_{\mathrm{z}}=1 \Rightarrow b_{w y}=\frac{1}{3}$
$b_{x x} b_{v y}=(1)\left(\frac{1}{3}\right)=\frac{1}{3}$
$\Rightarrow \frac{r_{z w}}{r_{x y}}=\frac{1}{3} \Rightarrow r_{z w}=\frac{r_{x y}}{3}=\frac{0.6}{3}=0.2$
$\mathrm{z}=\mathrm{x}+5 ; w=\frac{y}{3}$
$\Rightarrow \mathrm{b}_{\mathrm{z}}=1 \Rightarrow b_{w y}=\frac{1}{3}$
$b_{x x} b_{v y}=(1)\left(\frac{1}{3}\right)=\frac{1}{3}$
$\Rightarrow \frac{r_{z w}}{r_{x y}}=\frac{1}{3} \Rightarrow r_{z w}=\frac{r_{x y}}{3}=\frac{0.6}{3}=0.2$
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