capitulo 11

7,0
6,5
3,0
6,5
6,5
1,5
1,2
9
6,5
7,0
3,0
6,5
6,5
6,5
6,5
7,5
4,0
6,5
6,5
1,0
0,5
10
4,0
6,5
6,5
4,0
7,5
7,0
7,0
7,5
3,0
6,5
6,5
1,4
1,3
11
7,5
7,0
3,0
7,5
7,0
7,5
7,0
4,0
7,5
6,5
7,0
1,2
1,1
12
7,5
6,5
3,0
6,5
4,0
3,0
7,5
6,5
4,0
6,5
6,5
1,6
1,5
13
7,5
6,5
6,5
6,5
4,0
7,5
4,0
6,5
7,5
6,5
6,5
0,9
0,7
14
6,5
3,0
6,5
7,0
7,0
7,0
7,0
7,0
7,0
6,5
7,0
0,7
0,6
15
7,5
7,0
6,5
7,5
7,5
6,5
7,0
3,0
7,5
7,5
7,3
0,9
0,8
 Desvio padrão
0,3
0,4
0,4
Portanto, as estimativas de bootstrap dos parâmetros de interesse são dadas por:
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�PAGE �
Cap.11 – Pág.� PAGE �1�
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Gráf1
		0.00512
		0.02304
		0.03456
		0.02048
p
L(p)
11.1
		Distribuição amostral de p^
		# sucessos		0		1		2		3		4		5
		p^		0.0		0.2		0.4		0.6		0.8		1.0
		P(p^)		0.3277		0.4096		0.2048		0.0512		0.0064		0.0003
		
		E(p^) =		0.2
		Var(p^) =		0.032
11.2
		Var(p^) <= 1/(4n)
		
		n		10		25		100		400
		Limite superior de Var(p^)		0.025		0.01		0.0025		0.000625
11.2
		
Limite superior de Var(p^)
n
Limite superior de Var(p^)
11.5
						Estimadores
						t1		t2
		Resultados da simulação		Média		102		100
				Variância		5		10
				Mediana		100		100
				Moda		98		100
		Propriedades dos estimadores		Viés		2		0
				Variância		5		10
				EQM		9		10
11.6
		a)
						mi
						6		7		8		9		10
		t		yt		(yt-mi)^2		(yt-mi)^2		(yt-mi)^2		(yt-mi)^2		(yt-mi)^2
		1		3		9		16		25		36		49
		2		5		1		4		9		16		25
		3		6		0		1		4		9		16
		4		8		4		1		0		1		4
		5		16		100		81		64		49		36
				S(mi)		114		103		102		111		130
		
		
		
		
		
		
		
		
		
		
		
		
		
		
		
		
		S(mi) parece ser mínimo para mi aproximadamente igual a 7,5.
		
		(b)
		ybarra =		7.6
11.6
		
Xbarra
%
Histograma de Xbarra
11.7
		
mi
S(mi)
11.9
		Ano (t)		1967		1969		1971		1973		1975		1977		1979
		Inflação (yt)		128		192		277		373		613		1236		2639
		
		a)
		
		
		
		
		
		
		
		
		
		
		
		
		
		b)
		tbarra =		1973.00
		ybarra =		779.71
		soma(t*yt) =		10788548.00
		soma(t^2) =		27249215.00
		
		Estimativas de mínimos quadrados de alfa e beta
		alfa^ =		-350026.73
		beta^ =		177.80
		
		c)
		y(1981) =		2202.143
		
		d)
		Sim, pois o gráfico mostra que a inflação cresceu exponencialmente no período observado.
11.9
		
Inflação (yt)
Ano (t)
Inflação (yt)
11.10
		t		1		2		3		4		5		6		7		8		9		10
		xt		1.5		1.8		1.6		2.5		4.0		3.8		4.5		5.1		6.5		6.0
		yt		66.8		67.0		66.9		67.6		68.9		68.7		69.3		69.8		71.0		70.6
		
		xbarra =		3.73
		ybarra =		68.66
		soma(xt*yt) =		2586.43
		soma(xt^2) =		169.25
		
		Estimativas de mínimos quadrados de alfa e beta
		alfa^ =		65.513
		beta^ =		0.844
11.11
		n =		5
		x =		3
		
		Função de verossimilhança da distribuição Binomial(5;p)
		p		0 1/5		0 2/5		0 3/5		0 4/5
		L(p)		0.005		0.023		0.035		0.020
11.11
		
p
L(p)
11.14
		
11.15
												Intervalo de confiança
		Média amostral		Tamanho da amostra		Desvio padrão da população		Coeficiente de confiança				Limite inferior		Limite superior
		170		100		15		95%				167.06		172.94
		165		184		30		85%				161.82		168.18
		180		225		30		70%				177.93		182.07
11.16
		a)
		
												Intervalo de confiança
		xbarra		n		s		Coef. confiança				Limite inferior		Limite superior
		800		400		100		99%				787.06		812.94
		
		b)
		erro		n		s		zgama
		0.98		400		100		?
		
		zgama = erro*raiz(n)/s =>
		zgama =		0.196		=>
		gama =		15.54%
		
		
		c)
		erro		n		s		zgama
		7.84		?		100		1.96
		
		n = (s*zgama/erro)^2 =>
		n =		625
11.16
		
S^2
%
Distribuição de S^2
11.17
		
t
%
Histograma de t
11.18
		a)
		erro		n		s		zgama
		1		?		10		1.96
		
		n = (s*zgama/erro)^2 =>
		n =		384.14
		n aprox. =		385
		
		b)
		erro		n		s		zgama
		1		?		10		2.58
		
		n = (s*zgama/erro)^2 =>
		n =		663.49
		n aprox. =		664
11.19
		a)
		erro		n		sigma		zgama
		1		?		10		1.75
		
		n = (sigma*zgama/erro)^2 =>
		n =		306.49
		n aprox. =		307
		
		b)
												Intervalo de confiança
		xbarra		n		sigma		Coef. confiança				Limite inferior		Limite superior
		50		307		10		92%				49.00		51.00
11.20
										Intervalo de confiança						Intervalo de confiança conservador
		p^		n		Coef. confiança				Limite