I'm taking an introductory level course in statistics and the definitions of probability spaces and random variables are given in measure-theoretic terms. They are in this form.
I'd like to verify my understanding using the example below.
My understanding is that $\Omega$ is the set of $2^{10}$ different sequences of 10 heads or tails, and $E = \{0,1,2,3,4,5,6,7,8,9,10\}$. But I'm not sure what $\mathcal{F}$ (and consequently P) looks like. I also guess that a member of $\mathcal{E}$ in this case could be any subset of $E$?