7/23/2019 0parcial1 Bellaterra Tarda Respostes Mds

1/2

{x1, x2, x3, x4, . . . , xn} n5 2

1 = x1+ x2+ + xn2

n 2 =

x1+ x2+ x3+ x4+ x55

n= 5

B(1) = E(1) = E( x1+ x2+ + xn2n

) =

= 1n

(E(x1) + E(x2) + + E(xn2)) =

= 1

n(n 2) =2

n

V(1) = V(x1+ x2+ + xn2

n ) =

= 1

n2(V(x1) + V(x2) + V(xn2)) =

= 1

n2(n 2)2 = (n 2)

n2 2

B(2) = E(2) = E(x1+ x2+

+ x5

5 ) ==

1

5(E(x1) + E(x2) + + E(x5)) =

= 1

55 = 0

V(2) = V(x1+ x2+ + x5

5 ) =

= 1

52(V(x1) + V(x2) + + V(x5)) =

= 1

2552 =

2

5

EQM(1) = V(1) + B(1)2 =

(n 2)n2

2 + ( 2n

)2

EQM(2) = V(2) + B(2)2 =

2

5

2

EQM

Donat que a l'apartat a) lan=5, la soluci s -2/5*mu

Donat que a l'apartat a) la n=5la soluci s 3/25*sigma^2

Donat que a l'apartat n=5, la soluci s3/25*sigma^2 + 2/25*

7/23/2019 0parcial1 Bellaterra Tarda Respostes Mds

2/2

M QE(1) M QE(2)

limn

M QE(1) = limn

(n 2)n2

2 + ( 2n

)2 = 0

limn

M QE(2) = limn

2

5 =

2

5

X = 70 2 = 16

n= 50

[ X z12

2

n, X+ z1

2

2

n]

z12

= 0.05

z0.975 = 1.96

[70 1.96

16

50, 70 + 1.96

16

50]

[68.891, 71.108]

z12

2

n

1.96

216

n

1.96

16

n < 1.5 (1.96)(4)

1.5 27.318

n= 28

Caldria posar-hoen catal/castell,

EQM en comptesde MQE

Hauria de ser 16en comptes de 216