Question

(Logic Question\Probability theory) See next post.

Answer 1

I think this is a logic thing that I don't understand.This is taken from a book involving probability theory.
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\[0\le P(A) \le 1,A \in \mathcal{F}\]\[P( \Gamma)=1\]For a countable sum of mutually disjoint \[\{A1, A2,...\} \in \mathcal{F}:\]
\[P\{\cup_jA_j \}=\sum^{}_{j}P(A_j)\]Where,
gamma=sample space
curly F = random events
P(x) = the measure of probability that x will occur
A is a random event of curly F
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What I don't understand is the first part of the last line;\[P\{\cup_j A_j\}\]I've only ever seen the union symbol for the union between two sets, but here it seems there is only one set; the set of A_j. No set precedes the union symbol, which is what confuses me.

Answer 2

it's the union of all the A_j's. the union symbol with the subscript is like sigma, i.e. iterate over all values of the subscript

Answer 3

Thanks, I had a hunch that was the case.

Answer 4

trust ur own guts dude