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Expected values in Probability space
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[QUOTE="Lily@pie, post: 4366907, member: 314384"] I saw this example... Ω=N P(ω)=2[SUP]-ω[/SUP], ω in Ω X[SUB]n[/SUB](ω)=2[SUP]n[/SUP]δ[SUB]ω,n[/SUB] I can see that X[SUB]n[/SUB] is not convergent. But I'm not quite sure in computing the integrals... I'm very bad with the lim inf concept >_< So, I have written my attempt on evaluating the integrals and reasoning that I've used. My attempt, lim inf X[SUB]n[/SUB] =lim inf [2[SUP]n[/SUP]δ[SUB]ω,n[/SUB]] Since this takes in values 0 or 2[SUP]n[/SUP] =0 E[X[SUB]n[/SUB]] =I[SUB]P[/SUB][2[SUP]n[/SUP]δ[SUB]ω,n[/SUB]] = ∫2[SUP]n[/SUP]δ[SUB]ω,n[/SUB]2[SUP]-ω[/SUP]dω When ω=n, this reduces to ∫δ[SUB]ω,n[/SUB]dω =δ[SUB]ω,n[/SUB] I'm not very sure about the way I evaluate the integral. Would be very helpful for some guidance. [/QUOTE]
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Expected values in Probability space
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