# Problem about multivaluable distributions. (Hotelling distribution)

From $$n_1$$ p-dimensional random vectors: $$X_1,...,X_{n_1}$$ independents with $$X_i\sim N_p(\mu_1,\Sigma)$$ and $$n_2$$ random vectors with the same dimension: $$Y_1,...,Y_{n_2}$$ independents with $$Y_i\sim N_p(\mu_2,\Sigma)$$. Find a statistic wich estimate the difference between population means and wich has $$T^2$$ Hotelling distribution.

I really stuck on this problem in the way I don't know how to create this statistic.