Why does the covariance of the following two normal distributions, $X \thicksim N(67,20), Y \thicksim N(9,1),$ be $0?$ My simulations show that it should always be $0$ in these conditions, but I'm looking for some examples, proof or references.
Thank you
Since $X$ is the random variable that represents people's height and $Y$ is the random variable that represents the time people woke up. Intuitively speaking, two things should be independent because your height will not effect the time you wake up and the time you wake up will not effect your height. Since they are independent, we could say their covariance is zero. But we must be careful because there is no rigorous proof. It's more like an assumption.
