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G:\Statistiske grundbegreber-v8\s1v8-forside.wpd

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Flerdimensional statistisk variabel<br />

2 2<br />

= ( 0 −12 . ) ⋅ 0. 4 + ( 2 −12 . ) ⋅ 0. 6 = 0. 96 = 0. 97980<br />

a4) Vi finder<br />

E( X1 ⋅ X2) ≡ ∑ ∑ x1 ⋅ x2 ⋅ f ( x1, x2)<br />

= 00 ⋅ ⋅ f ( 00 , ) + 10 ⋅ ⋅ f ( 10 , ) +<br />

x1<br />

x2<br />

2⋅0⋅ f (,) 20 + 0⋅2⋅ f (,) 02 + 1⋅2⋅ f (,) 12 + 2⋅ 2⋅ f (,) 22<br />

= 0⋅ 02 . + 0⋅ 01 . + 0⋅ 01 . + 0⋅ 01 . + 2⋅ 02 . + 4⋅ 03 . = 16 .<br />

b1) Stikprøvens x1 -værdier 1, 0, 2, 2, 1, 2, 0, 2, 0, 2 kan indtastes på en lommeregner, der finder gennemsnittet<br />

og standardafvigelsen s1 som tilnærmelser til middelværdi µ 1 og spredning σ1 for X 1 . Man finder:<br />

µ 1 ≡ E( X1) ≈ x1=<br />

12 . , σ1 = σ(<br />

X1) ≈ s1<br />

= 09189 . .<br />

x 2<br />

Analogt indtastes stikprøvens - værdier 2, 0, 2, 2, 0, 2, 2, 2, 2, 2, og man finder<br />

µ 2 ≡ E( X2) ≈ x2=<br />

16 . ,<br />

σ = σ(<br />

X ) ≈ s = .<br />

126<br />

2 2 2 08433<br />

Det ses, at estimaterne har en vis lighed med de eksakte værdier i spørgsmål a3).<br />

.<br />

x1

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