For those curious about the details of this, I found this interesting article: https://www.quantamagazine.org/statistician-proves-gaussian-correlation-inequalit

For those curious about the details of this, I found this interesting article: https://www.quantamagazine.org/statistician-proves-gaussian-correlation-inequality-20170328/ https://www.quantamagazine.org/statistician-proves-gaussian-....