I'm new to statistics and and I need some help:
Let $X_1,...X_n$~$N(\mu_x,\sigma^2)$, $Y_1,...Y_m$~$N(\mu_y,\sigma^2)$.
All r.vs. are i.i.d and $\mu_x,\mu_y,\sigma$ are unknown
I was told that $S_p^2=(S_x^2(n-1)+S_y^2(m-1))/(n+m-2)$ is an unbiased estimator for the sample covariance.
I think I'm confused over definitions because to my best of knowledge covariance cannot be calculated when $n\not=m$. Am I correct? if so what is the above actually an unbiased estimator of?