The random variables $Y_{1}$ and $Y_{2}$ follow the bivariate normal distribution in $(2.74) .$ Show that if $\rho_{12}=0, Y_{1}$ and $Y_{2}$ are independent random variables.
Added by Sarah W.
Step 1
Step 1:** Given that the bivariate normal distribution for $Y_{1}$ and $Y_{2}$ is $f(y_{1}, y_{2}) = \frac{1}{2\pi \sigma_{1} \sigma_{2} \sqrt{1-\rho_{12}^2}} \exp\left(-\frac{1}{2(1-\rho_{12}^2)}\left(\frac{(y_{1}-\mu_{1})^2}{\sigma_{1}^2} - Show moreā¦
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