Question

The coefficient of correlation between the values denoted by $X$ and $Y$ is $0.5$. The mean of $X$ is $3$ and that of $Y$ is $5$. Their standard deviations are $5$ and $4$ respectively. Find:
The expected value of $X$, when $Y$ is given $9$

Answer 1

$\overline{x}=3,\overline{y}=5,{\sigma }_x=5,{\sigma }_y=4,r=0.5$
$b_{yx}=r\cdot \frac{{\sigma }_y}{{\sigma }_x}=0.5\times \frac{4}{5}=0.4$,
$b_{xy}=r\cdot \frac{{\sigma }_x}{{\sigma }_y}=0.5\times \frac{5}{4}=0.625$
$y=9$
$x=0.625\times 9-0.125=5.625-0.125=5.5$