Below, you will investigate the location, scale, and replication properties of the KDE with a Gaussian kernel.

To be clear, you will consider how the KDE at a fixed point y$0$ is impacted when the population P is modified.

$($a$)[2$ points$]$ Determine whether the kernel density estimator $$fh$($y$0)$ with a Gaussian kernel is location

invariant, location equivariant, or neither.

$($b$)[2$ points$]$ Determine whether the kernel density estimator $$fh$($y$0)$ with a Gaussian kernel is scale

invariant, scale equivariant, or neither.

$3$