2 problems

Let $Y_1,\ldots,Y_n$ be independent identically distributed samples from a Gaussian distribution, let $\mathbf{y}=(Y_1,\ldots,Y_n)$, let $\bar{\mathbf{y}}$ be their sample mean, an…

Let $\mathbf{W}^{(n)}=\mathrm{W}_2^2(\hat\mu^{1,(n)},\hat\nu^{1,(n)})$ be the squared Wasserstein distance between two empirical samples of size $n$ from the standard normal distri…