Grinstead and Snells book, Introduction to Probability, page 144:
Here is a number of short questions I have about this text:
0) The authors say that they consider "special classes of random variables", one such classe being the class of indepedent trails. I think this is imprecise: They should have said "classes of sequences of random variables". What do you think ?
1) The $X_j$ are functions $X_j:R\times R\times \ldots \times R \rightarrow \mathbb{R}$, right ?
2) They should have specified that $R\subseteq \mathbb{R}$ since otherwise the $j$-th projection isn't well defined: $X_j(\Omega)\subseteq \mathbb{R}$, but it $R\ni \omega_j \not\in \mathbb{R}$.
3) On the second line from below shouldn't it say "outcome $(\omega_1,\ldots,\omega_n)$, rather then $(r_1,\ldots,r_n)$ ? (The $r$'s are also already used to define $R=\{r_1,\ldots,r_s\}$)
4) Most important Is it that trivial to see (penultimate line) that the random variables $X_1,\ldots,X_n$ form an independent trials process ? It is indeed easy to see, that they have the same distribution, but proving that they are mutually independent does require some work!