Here's the question bank on all the mathematics topics.
For two correlated variables x and y, if coefficient of correlation between x and y is 0.8014, variance of x and y are 16 and 25 respectively. Then the covariance between x and y is:
Concept:Formulas used:\({\rm{r}}\left( {{\rm{x}},{\rm{y}}} \right) = \frac{{{\rm{\;Cov}}\left( {{\rm{x}},{\rm{y}}} \right)}}{{{\rm{\sigma }}\left( {\rm{x}} \right){\rm{\sigma }}\left( {\rm{y}} \right)}}\)Where,r (x, y) is the Correlation coefficient between x and yCov(x, y) Covariance of x and y?(x), ?(y) is the standard deviation of x, y respectivelyCalculation:Given:Correlation coefficient between x and y, r(x, y) = 0.8014Covariance of x and y, Cov(x, y) = ?standard deviation y, ?(y) = (25)1/2 = 5standard deviation x, ?(x) = (16)1/2 = 4We know that, \({\rm{r}}\left( {{\rm{x}},{\rm{y}}} \right) = \frac{{{\rm{\;Cov}}\left( {{\rm{x}},{\rm{y}}} \right)}}{{{\rm{\sigma }}\left( {\rm{x}} \right){\rm{\sigma }}\left( {\rm{y}} \right)}}\)\(Cov(x,y)=r(x,y)× \sigma(x)\sigma(y)\)Cov (x, y) = 0.8014 × 5 × 4 = 16.028
Scan QR code to download our App for
more exam-oriented questions
OR
To get link to download app