My book has a description in the setting of a coin flip experiment. It says, if we let "heads" equal 1 and "tails" equal 0, then we get a random variable:(adsbygoogle = window.adsbygoogle || []).push({});

[itex]X=X(\omega)\epsilon\{0,1\}[/itex]

where [itex]\omega[/itex] belongs to the outcome space [itex]\Omega=\{heads, tails\}[/itex]

Under the innocuous subheading:

"Which are the most likely [itex]X(\omega)[/itex], what are they concentrated around, what are their spread?

the book says that to approach those problems, one first collects "good" subsets of [itex]\Omega[/itex] in a class F, where F is a [itex]\sigma[/itex]-field. Such a class is supposed to contain all interesting events. Certainly, {w:X(w)=0}={tail} and {w:X(w)=1}={head} must belong to F, but also the union, difference, and intersection of any events in F and its complement the empty set. If A is an element of F, so is it's complement, and if A,B are elements of F, so are A intersection B, A union B, A union B complement, B union A complement, A intersection B complement, B intersection A complement, etc.

Whaaa? What's all that [itex]\sigma[/itex]-field stuff got to do with the probabilites of X(w)? Also, if A and B are a member of a class F, isn't A union B also automatically a member of the class F, as well as A intersection B, etc.?

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# Some basic set questions

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