Twice, first set σ = 3 and then repeat again with σ = 6. How does the scatter of points change as σ changes? But this time set X to have a standard normal distribution and e to have a Cauchy...

Twice, first set σ = 3 and then repeat again with σ = 6. How does the scatter of points change as σ changes?

But this time set X to have a standard normal distribution and e to have a Cauchy distribution (set σ = 1). The easy way to generate a Cauchy is to generate two vectors V₁
and V₂
of standard normal random numbers, and then set e = V₁/V₂. With this setup, the values you generate are not bivariate normal because the Cauchy does not have a population mean or variance.