Two real-valued RVs, X and Y, have joint PDF 1 p(x1, x2) = exp 2TV1- 2(1 - r?) where -1

Two real-valued RVs, X and Y, have joint PDF<br>1<br>p(x1, x2) =<br>exp<br>2TV1-<br>2(1 - r?)<br>where -1 <r< 1. Prove that cach of X and Y is normally distributed with mean 0 and<br>variance 1.<br>Prove that the number r is the correlation coefficient of X and Y.<br>

Extracted text: Two real-valued RVs, X and Y, have joint PDF 1 p(x1, x2) = exp 2TV1- 2(1 - r?) where -1 <>< 1.="" prove="" that="" cach="" of="" x="" and="" y="" is="" normally="" distributed="" with="" mean="" 0="" and="" variance="" 1.="" prove="" that="" the="" number="" r="" is="" the="" correlation="" coefficient="" of="" x="" and="">

Jun 11, 2022

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Two real-valued RVs, X and Y, have joint PDF 1 p(x1, x2) = exp 2TV1- 2(1 - r?) where -1

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