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I am trying to learn gaussian process, using this lecture from Richard Turner: https://youtu.be/92-98SYOdlY

enter image description here

I don't understand this part in the sense that he stresses the importance of the line (on the right side) always kinda straight, he says: "because the 2 variables are correlated with one another, the bar tends to move up and down together" and then: "the bar moves up and down, there is a bit of flexibility because the 2 variables are only correlated 0.9".

Why he says it? we can have correlation 1, with values being

[1, 10000] [2, 20000] [3, 30000]

and so on... and the correlation would be 1... and the line would not be straight... I see the line straight on the right only because he chose 0 as a mean for both variables...

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Looking at the covariance matrix, both marginal variables have been transformed to their z-scores: $\frac{x-\bar{x}}{s}$. This means that both marginal variables have variances of 1. Otherwise, you’d be correct.

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