Expectation of Maximum and Minimum of Asymptotic Exponentials

Suppose we have $K$ series of positive random variables $\{X_{k,n},k=1,\dots, K, n\geq 1\}$. Series are independent of each other, but for each $n$, $X_{k,n},k=1,\dots, K$ are identically distributed.

We know that $X_{k,n}\to Y_k$ in distribution for each $k$, where $Y_k$ follows an exponential distribution. Moreover, we know that $E X_{k,n}\to EY_k$ for each $k$.

I wonder if we could have some conclusion on $E\max_k X_{k,n}$ and $E\min_k X_{k,n}$,

I appreciate any guidance!