The Law Of Large Numbers Pdf Download
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Pr,,,(,,,lim,,,n,,,→,,,∞,,,X,,,,,,n,,,=,,,μ,,,),,,=,,,1.,,,In,realistic,situations,,chemists,can,describe,diffusion,as,a,deterministic,macroscopic,phenomenon,(see,Fick's,laws),,despite,its,underlying,random,nature.,Strong,law[edit].,{displaystyle,,2n/log(n+1).},,At,,each,,stage,,,the,,average,,will,,be,,normally,,distributed,,(since,,it,,is,,the,,average,,of,,a,,set,,of,,normally,,distributed,,variables).,,Intuitively,,expected,absolute,difference,grows,,but,at,a,slower,rate,than,the,number,of,flips,,as,the,number,of,flips,grows.,φ,,,X,,,,,,n,,,(,,,t,,,),,,=,,,[,,,φ,,,X,,,(,,,t,,,n,,,),,,],,,n,,,=,,,[,,,1,,,+,,,i,,,μ,,,t,,,n,,,+,,,o,,,(,,,t,,,n,,,),,,],,,n,,,→,,,e,,,i,,,t,,,μ,,,,,,,as,,,n,,,→,,,∞,,,.,,,Geyer,,Charles.,The,,independence,,of,,the,,random,,variables,,implies,,no,,correlation,,between,,them,,,and,,we,,have,,that.,,
But,,it,,also,,applies,,in,,some,,other,,cases.,,Probability,,,and,,,Random,,,Processes,,,,2nd,,,Edition.,,,{displaystyle,operatorname,{P},(left{overline,{X}}{n}-mu,rightgeq,varepsilon,)leq,{frac,{sigma,^{2}}{nvarepsilon,^{2}}}.},.,50.,,,MathWorld.,{displaystyle,Pr(X-mu,geq,ksigma,)leq,{frac,{1}{k^{2}}}.},.,(Lebesgue,,,integrability,,,of,,,Xj,,,means,,,that,,,the,,,expected,,,value,,,E(Xj),,,exists,,,according,,,to,,,Lebesgue,,,integration,,,and,,,is,,,finite.).,,,
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