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NDA 2019
Exam
NDA
Year
2019
Subject
Mathematics
Chapter
Statistics

NDA 2019 · Mathematics · Statistics

Let the correlation coefficient between X and Y be 0.6. Random...

Let the correlation coefficient between X and Y be 0.6. Random variables ZZ and WW are defined as Z=X+5Z=X+5 and W=Y3\mathrm{W}=\frac{Y}{3}. What is the correlation coefficient between Z and W?\mathrm{W} ?

Options

  1. A0.1
  2. B0.2
  3. C0.36
  4. D0.6

Correct answer

D. 0.6

Step-by-step solution

Given, rxy=0.6r_{x y}=0.6z=x+5;w=y3⇒bzx=1⇒bwy=13\begin{aligned} & \mathrm{z}=\mathrm{x}+5 ; w=\frac{y}{3} \\ & \Rightarrow \mathrm{ b}_{\mathrm{zx}}=1 \Rightarrow b_{w y}=\frac{1}{3}\end{aligned}$\begin{aligned} & b_{x y}=b_{z x} b_{w y}=(1)\left(\frac{1}{3}\right)=\frac{1}{3} \\ & \Rightarrow \frac{\mathrm{ b}_{z w}}{\mathrm{ b}_{x y}}=\frac{1}{3} \Rightarrow \mathrm{ b}_{z w}=\frac{\mathrm{b}_{x y}}{3}=\frac{0.6}{3}=0.2\end{aligned}
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