bivariate normal distribution question

Alex C

Member
My question is based on the defintion available at https://www.statisticshowto.datasciencecentral.com/bivariate-normal-distribution/ which says:

1. What is a Bivariate Normal Distribution?
The “regular” normal distribution has one random variable; A bivariate normal distribution is made up of two independent random variables. The two variables in a bivariate normal are both are normally distributed, and they have a normal distribution when both are added together.

I don't understand why they say two independent variables, when everywhere else it is said that if X and Y follow a bivariate normal distribution they are independent only if the correlation coefficient rho=0. Am I misunderstanding something?

katxt

Member
The x's are independent of the other x's, and the y's are independent of each other, but the x's and the y's may be correlated with each other.
The x and y numbers are in pairs. They are not normally added together. If you plot the pairs on a graph, they look like an ellipse of random points.

hlsmith

Less is more. Stay pure. Stay poor.
This was the first image I saw on the web: