Question
Random variables $X$ and $Y$ are mutually dependent variables. Following data is collected from a random sample of $10$ observations: $\Sigma x=360: \Sigma y=450 ; \operatorname{Cov}(x, y)=90 ; S_{x}=9, S_{y}=12$
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| Marks in Economics | $60$ | $30$ | $10$ | $20$ | $30$ | $50$ | $30$ | $40$ |
| Marks in Dancing skill | $80$ | $20$ | $60$ | $40$ | $12$ | $28$ | $20$ | $15$ |
| Year | $2008$ | $2009$ | $2010$ | $2011$ | $2012$ | $2013$ | $2014$ |
| Average annual income $(Rs. 10,000)$ | $36$ | $40$ | $48$ | $52$ | $60$ | $80$ | $95$ |
| years | $2015$ | $2016$ | $2017$ | $2018$ | $2019$ | $2020$ |
| Index numbers of sale | $110$ | $112$ | $109$ | $108$ | $105$ | $111$ |