Felfortplantningsformlerna - Matematiska institutionen - Stockholms ...

7 FACIT 137 FacitF1) σ ≈ 0.01πd 2F2) E [X] ≈ 10 −p σ X ≈ σ·log(10)10 pF4) (a) Exakt: E [Y ] = log((1+ɛ)/(1−ɛ))2ɛApprox: E [Y ] = 1F5)Det relativa felet blir ungefär 9.0% (ɛ = 0.50) , 2.1% (ɛ = 0.25), 0.3% (ɛ = 0.10) ,respektive 0.1% (ɛ = 0.05).(b) Exakt: Var(Y ) ≈ 3.383 · 10 −3F6) E [g] ≈ 4π2 lt 2Approx: Var(Y ) ≈ 3.333 · 10 −3E [Y − X] = µ 2 − µ 1 Var(Y − X) = 11.45E [Y/X] ≈ µ 2µ 1Var(Y/X) ≈ (7.84µ2 2 + 9.61µ 2 1 − 6µ 1 µ 2 )µ 4 1Var(g) ≈ Var(l) · 16π4t 4 + Var(t) · 64π4 l 2t 6 (σ g ≈ 19.64)F7) (a) Om X, Y antar värdena 1, 2:Exakt: E [Y/X] = 9/8 = 1.125Approx: E [Y/X] ≈ 1Om X, Y antar värdena 11, 12:Exakt: E [Y/X] = 529/528 ≈ 1.0019Approx: E [Y/X] ≈ 1Om X, Y antar värdena 0.5, 1:Exakt: E [Y/X] = 9/8 = 1.125Approx: E [Y/X] ≈ 1(b) Om X, Y antar värdena 1, 2:Exakt: Var(Y/X) = 19/64 ≈ 0.297Approx: Var(Y/X) = 2/9 ≈ 0.222Om X, Y antar värdena 11,12:Exakt: Var(Y/X) ≈ 0.003799