I'm studying by Statistical Inference by Casella and Berger and on page 225, I didn't understand why he expected the $F$ distribution behaved in this way (see the highlighted part in the end of the image).
Let's $X_1,\ldots,X_n$ and $Y_1,\ldots,Y_m$ random samples of $N(\mu_X,\sigma^2_X)$ and $N(\mu_Y,\sigma^2_Y)$ respectively. So why it's expected the $F$ distribution goes to $1$ for a large $m$ and why this is important? (I'm sorry it's the first time I'm studying $F$ distributions, I'm not aware why it's so important and what the important features are)