Undergrad Sampling from a multivariate Gaussian distribution

[asilvester635]

I was watching a lecture on youtube about linear regression and there's a section where it had the statement below (written in purple). Does multiplying by sigma rotate the distribution to make it look like x - N(mew, sigma^2)? Mew in this case is 0 so it doesn't shift the distribution.

 

[EngWiPy]

To me $x$ and $y$ are just dummy variables, and both are on the x-axis, or should be, because the y-axis represents the distribution of the probability density, which in this case is a normal distribution. $y$ has its peak at zero on the x-axis, and $x$ has its peak at $\mu$ on the x-axis.

 

[Stephen Tashi]

Sampling from a multivariate Gaussian distribution

The example you gave doesn't illustrate a "multivariate" distribution. It illustrates two univariate distributions.