Resoluções lista 03 IPE

Resoluções lista 03 IPE

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BC0406: Intr. à Prob. e à Estatística UFABC Resolução da Lista 03 v2 
 
 
Fernando Freitas Alves fernando.freitas@aluno.ufabc.edu.br 04/03/13 \u2013 pág. 1/11 
1. 
a) 
(15
3
)
(
26
3
)
=
15 · 14 · 13
3!
26 · 25 · 24
3!
=
7
2 · 5 · 4
=
7
40
 
b) 
1 \u2212
(15
3
)
(
26
3
)
=
33
40
 
c) 
(11
2
) (15
1
)
(
26
3
)
=
11 · 10
2! ·
15
1!
26 · 25 · 24
3!
=
11 · 3
13 · 8
=
33
104
 
 
2. 
\u2211 \ud835\udc565\ud835\udc56=1
62
=
1+ 2 + 3 + 4 + 5
6 · 6
=
5
12
 
 
3. 
6 · 5 · 4 · 3
64
=
6 · 5 · 4 · 3
6 · 6 · 6 · 6
=
5
6 · 3
=
5
18
 
 
4. 
a) 
\ud835\udc5bº \ud835\udc51\ud835\udc52 \ud835\udc52\ud835\udc63\ud835\udc52\ud835\udc5b\ud835\udc61\ud835\udc5c\ud835\udc60 \ud835\udc50\ud835\udc5c\ud835\udc5a \ud835\udc5b\ud835\udc52\ud835\udc5b\u210e\ud835\udc62\ud835\udc5a\ud835\udc4e \ud835\udc50\ud835\udc4e\ud835\udc5f\ud835\udc4e
\ud835\udc5bº \ud835\udc51\ud835\udc52 \ud835\udc52\ud835\udc63\ud835\udc52\ud835\udc5b\ud835\udc61\ud835\udc5c\ud835\udc60 \ud835\udc61\ud835\udc5c\ud835\udc61\ud835\udc4e\ud835\udc56\ud835\udc60
= \ud835\udc5d\ud835\udc5b = (
1
2
)
7
=
1
128
 
b) 
\ud835\udc5bº \ud835\udc51\ud835\udc52 \ud835\udc52\ud835\udc63\ud835\udc52\ud835\udc5b\ud835\udc61\ud835\udc5c\ud835\udc60 \ud835\udc50\ud835\udc5c\ud835\udc5a 3 \ud835\udc50\ud835\udc4e\ud835\udc5f\ud835\udc4e\ud835\udc60
\ud835\udc5bº \ud835\udc51\ud835\udc52 \ud835\udc52\ud835\udc63\ud835\udc52\ud835\udc5b\ud835\udc61\ud835\udc5c\ud835\udc60 \ud835\udc61\ud835\udc5c\ud835\udc61\ud835\udc4e\ud835\udc56\ud835\udc60
= (
\ud835\udc58
\ud835\udc5b
)\ud835\udc5d\ud835\udc5b = (
7
3
) (
1
2
)
7
=
35
128
 
c) 
\u2211(\ud835\udc58
\ud835\udc56
) \ud835\udc5d\ud835\udc5b
7
\ud835\udc56=3
= ((
7
3
) + (
7
4
) + (
7
5
) + (
7
6
) + (
7
7
))(
1
2
)
7
=
99
128
 
 
BC0406: Intr. à Prob. e à Estatística UFABC Resolução da Lista 03 v2 
 
 
Fernando Freitas Alves fernando.freitas@aluno.ufabc.edu.br 04/03/13 \u2013 pág. 2/11 
5. 
(10 \u2212 2
5
)
(
10
5
)
=
(10 \u2212 2
3
)
(
10
5
)
=
(8
3
)
(
10
5
)
 
 
6. 
a) 
\u2119[\ud835\udc34 \u222a \ud835\udc35] = \u2119[\ud835\udc34] + \u2119[\ud835\udc35] = 0,3 + 0,5 = 0,8 
b) 
\u2119[\ud835\udc34 \u2229 \ud835\udc35\ud835\udc36] = \u2119[\ud835\udc34] = 0,3 
c) 
\u2119[\ud835\udc34 \u2229 \ud835\udc35] = 0 
 
7. Resolução errada: não consideram a chance de vir outra jogada em um jogada específica. 
8. 
\ud835\udc5d = 
=
82 · 72 · 62 · 52 · 42 · 32 · 22 · 12
82 · (82 \u2212 1) · (82 \u2212 2) · (82 \u2212 3) · (82 \u2212 4) · (82 \u2212 5) · (82 \u2212 6) · (82 \u2212 7)
 
=
82 · 72 · 62 · 52 · 42 · 32 · 22 · 12
(8
2
8
) 8!
 
=
560
61474519
 
= 0,000911% 
 
9. 
\ud835\udc5d = 
=
(4
1
) (4 × 4
1
)
(52
2
)
 
=
32
663
 
= 4,83% 
BC0406: Intr. à Prob. e à Estatística UFABC Resolução da Lista 03 v2 
 
 
Fernando Freitas Alves fernando.freitas@aluno.ufabc.edu.br 04/03/13 \u2013 pág. 3/11 
 
10. 
a) \ud835\udc5d(\ud835\udc56) =
\ud835\udc56
20
=
{
 
 
 
 
 
1 20\u2044
2 20\u2044
3 20\u2044
4 20\u2044
5 20\u2044
 
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 1
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 2
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 3
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 4
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 5
 
 
b) \ud835\udc5d(\ud835\udc56) =
\ud835\udc56×\ud835\udc5b\ud835\udc56
\u2211 \ud835\udc56×\ud835\udc5b\ud835\udc56
5
\ud835\udc56=1
=
{
 
 
 
 
 
4 × 1 48\u2044
8 × 2 48\u2044
5 × 3 48\u2044
2 × 4 48\u2044
1 × 5 48\u2044
 
= 4 48\u2044
= 16 48\u2044
= 15 48\u2044
= 8 48\u2044
= 5 48\u2044
 
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 1
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 2
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 3
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 4
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 5
; \ud835\udc5b\ud835\udc56 = \ud835\udc5bº \ud835\udc53\ud835\udc4e\ud835\udc5aí\ud835\udc59\ud835\udc56\ud835\udc4e\ud835\udc60 \ud835\udc50/ \ud835\udc56 \ud835\udc53\ud835\udc56\ud835\udc59\u210e\ud835\udc5c\ud835\udc60 
 
11. 
\ud835\udc5d(\ud835\udc56) =
\ud835\udc5b\ud835\udc56
62
=
{
 
 
 
 
 
 
 
 
 
 
 
1 36\u2044
2 36\u2044
3 36\u2044
4 36\u2044
5 36\u2044
6 36\u2044
5 36\u2044
4 36\u2044
3 36\u2044
2 36\u2044
1 36\u2044
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 2
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 3
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 4
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 5
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 6
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 7
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 8
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 9
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 10
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 11
 \u2044 \ud835\udc60\ud835\udc52 \ud835\udc56 = 12
 ; \ud835\udc5b\ud835\udc56 = \ud835\udc5bº \ud835\udc53\ud835\udc4e\ud835\udc5aí\ud835\udc59\ud835\udc56\ud835\udc4e\ud835\udc60 \ud835\udc50/ \ud835\udc56 \ud835\udc53\ud835\udc56\ud835\udc59\u210e\ud835\udc5c\ud835\udc60 
 
12. 
\u2119(\ud835\udc38\ud835\udc5b) = 
= \ud835\udc5d × \ud835\udc5e\ud835\udc5b\u22121 
=
\ud835\udc465
62
 (1 \u2212
\ud835\udc465 + \ud835\udc467
62
)
\ud835\udc5b\u22121
 
=
4
36
 (1 \u2212
4 + 6
36
)
\ud835\udc5b\u22121
 
=
1
9
 (
13
18
)
\ud835\udc5b\u22121
 
 
\u2119(\ud835\udc38\u221e) = 
BC0406: Intr. à Prob. e à Estatística UFABC Resolução da Lista 03 v2 
 
 
Fernando Freitas Alves fernando.freitas@aluno.ufabc.edu.br 04/03/13 \u2013 pág. 4/11 
= \u2211\u2119(\ud835\udc38\ud835\udc5b)
\u221e
\ud835\udc5b=1
 
= \u2211
1
9
 (
13
18
)
\ud835\udc5b\u22121\u221e
\ud835\udc5b=1
 
=
1
9
\u2211(
13
18
)
\ud835\udc5b\u22121\u221e
\ud835\udc5b=1
 
=
1
9
\u2211(
13
18
)
\ud835\udc65\u221e
\ud835\udc65=0
 ; \ud835\udc65 = \ud835\udc5b \u2212 1 
\u3a3n = \ud835\udc5e + \ud835\udc5e
2 +\u22ef+ \ud835\udc5e\ud835\udc5b 
\ud835\udc5e\u3a3n = \ud835\udc5e
2 + \ud835\udc5e3 +\u22ef+ \ud835\udc5e\ud835\udc5b+1 
\u3a3n \u2212 \ud835\udc5e\u3a3n = \ud835\udc5e \u2212 \ud835\udc5e
\ud835\udc5b+1 
\u3a3n =
\ud835\udc5e \u2212 \ud835\udc5e\ud835\udc5b+1
1 \u2212 \ud835\udc5e
 
\u3a3n =
1\u2212 \ud835\udc5e\ud835\udc5b
1 \ud835\udc5e\u2044 \u2212 1
 
\ud835\udc5e < 1 
\ud835\udc5b \u2192 \u221e \u21d2 \ud835\udc5e\ud835\udc5b \u2192 0 
\u3a3\u221e =
1
1 \ud835\udc5e\u2044 \u2212 1
 
=
1
9
×
1
1 (
13
18
)\u2044 \u2212 1
 
=
1
9
×
18
18 \u2212 13
 
=
2
18 \u2212 13
 
=
\ud835\udfd0
\ud835\udfd3
 
 
13. 
\u2119(\ud835\udc34 \ud835\udc5d\ud835\udc52\ud835\udc54\ud835\udc4e\ud835\udc5f \ud835\udc4e\ud835\udc5b\ud835\udc61\ud835\udc52\ud835\udc60 \ud835\udc51\ud835\udc5c \ud835\udc35) = 
=
1
10!
(\u2211\u2115(\ud835\udc5b\ud835\udc52\ud835\udc54\ud835\udc5f\ud835\udc4e\ud835\udc60 \ud835\udc5d\ud835\udc5c\ud835\udc60\ud835\udc60í\ud835\udc63\ud835\udc52\ud835\udc56\ud835\udc60 \ud835\udc4e\ud835\udc5b\ud835\udc61\ud835\udc52\ud835\udc60 \ud835\udc51\ud835\udc52 \ud835\udc56) × \u2115(\ud835\udc63\ud835\udc52\ud835\udc5f\ud835\udc5a\ud835\udc52\ud835\udc59\u210e\ud835\udc4e\ud835\udc60 \ud835\udc5d\ud835\udc5c\ud835\udc60\ud835\udc60í\ud835\udc63\ud835\udc52\ud835\udc56\ud835\udc60)
7
\ud835\udc56=0
× \u2115(\ud835\udc4f\ud835\udc5c\ud835\udc59\ud835\udc4e\ud835\udc60 \ud835\udc5f\ud835\udc52\ud835\udc60\ud835\udc61\ud835\udc4e\ud835\udc5b\ud835\udc61\ud835\udc52\ud835\udc60)) 
BC0406: Intr. à Prob. e à Estatística UFABC Resolução da Lista 03 v2 
 
 
Fernando Freitas Alves fernando.freitas@aluno.ufabc.edu.br 04/03/13 \u2013 pág. 5/11 
=
1
10!
(\u2211\ud835\udc56! (
7 \u2212 \ud835\udc56
\ud835\udc56
) × (
3
1
) × (10 \u2212 (2\ud835\udc56 + 1))!
7
\ud835\udc56=0
) 
=
1
10!
(3 × (10 \u2212 1)! + 7 · 6 × 3 × (10 \u2212 (2 + 1))! + 7 · 6 · 5 · 4 × 3
× (10 \u2212 (4 + 1))! + 7 · 6 · 5 · 4 · 3 · 2 × 3 × (10 \u2212 (6 + 1))! + 7 · 6
· 5 · 4 · 3 · 2 · 1 · 0 × 3 × (10 \u2212 (8 + 1))!) 
=
1
10!
(3 × 9! + 7 · 6 × 3 × 7! + 7 · 6 · 5 · 4 × 3 × 5! + 7! × 3 × 3!) 
=
1
10!
(3 × 9! + 7 · 6 × 3 × 7! + 7 · 6 · 5 · 4 × 3 × 5! + 7! × 3 × 3!) 
=
\ud835\udfd5
\ud835\udfcf\ud835\udfd0
 
 
14. 
a) \u2119(2 \ud835\udc56\ud835\udc54\ud835\udc62\ud835\udc4e\ud835\udc56\ud835\udc60 \ud835\udc60\ud835\udc52\ud835\udc5a \ud835\udc5f\ud835\udc52\ud835\udc5d\ud835\udc5c\ud835\udc60\ud835\udc56çã\ud835\udc5c) = 
=
\u2115(2 \ud835\udc4f\ud835\udc5f\ud835\udc4e\ud835\udc5b\ud835\udc50\ud835\udc4e\ud835\udc60 \ud835\udc60\ud835\udc52\ud835\udc5a \ud835\udc5f\ud835\udc52\ud835\udc5d\ud835\udc5c\ud835\udc60\ud835\udc56çã\ud835\udc5c) + \u2115(2 \ud835\udc5b\ud835\udc52\ud835\udc54\ud835\udc5f\ud835\udc4e\ud835\udc60 \ud835\udc60\ud835\udc52\ud835\udc5a \ud835\udc5f\ud835\udc52\ud835\udc5d\ud835\udc5c\ud835\udc60\ud835\udc56çã\ud835\udc5c)
\u2115(2 \ud835\udc5e\ud835\udc62\ud835\udc4e\ud835\udc56\ud835\udc60\ud835\udc5e\ud835\udc62\ud835\udc52\ud835\udc5f \ud835\udc60\ud835\udc52\ud835\udc5a \ud835\udc5f\ud835\udc52\ud835\udc5d\ud835\udc5c\ud835\udc60\ud835\udc56çã\ud835\udc5c)
 
=
\ud835\udc5b(\ud835\udc5b \u2212 1) + \ud835\udc5a(\ud835\udc5a \u2212 1)
(\ud835\udc5b +\ud835\udc5a)(\ud835\udc5b +\ud835\udc5a \u2212 1)
 
 
b) \u2119(2 \ud835\udc56\ud835\udc54\ud835\udc62\ud835\udc4e\ud835\udc56\ud835\udc60 \ud835\udc50\ud835\udc5c\ud835\udc5a \ud835\udc5f\ud835\udc52\ud835\udc5d\ud835\udc5c\ud835\udc60\ud835\udc56çã\ud835\udc5c) = 
=
\u2115(2 \ud835\udc56\ud835\udc54\ud835\udc62\ud835\udc4e\ud835\udc56\ud835\udc60 \ud835\udc50\ud835\udc5c\ud835\udc5a \ud835\udc5f\ud835\udc52\ud835\udc5d\ud835\udc5c\ud835\udc60\ud835\udc56çã\ud835\udc5c) + \u2115(2 \ud835\udc56\ud835\udc54\ud835\udc62\ud835\udc4e\ud835\udc56\ud835\udc60 \ud835\udc50\ud835\udc5c\ud835\udc5a \ud835\udc5f\ud835\udc52\ud835\udc5d\ud835\udc5c\ud835\udc60\ud835\udc56çã\ud835\udc5c)
\u2115(2 \ud835\udc56\ud835\udc54\ud835\udc62\ud835\udc4e\ud835\udc56\ud835\udc60 \ud835\udc50\ud835\udc5c\ud835\udc5a \ud835\udc5f\ud835\udc52\ud835\udc5d\ud835\udc5c\ud835\udc60\ud835\udc56çã\ud835\udc5c)
 
=
\ud835\udc5b2 +\ud835\udc5a2
(\ud835\udc5b +\ud835\udc5a)2
 
 
c) \u22a2 : \u2119(2 \ud835\udc56\ud835\udc54\ud835\udc62\ud835\udc4e\ud835\udc56\ud835\udc60 \ud835\udc50\ud835\udc5c\ud835\udc5a \ud835\udc5f\ud835\udc52\ud835\udc5d\ud835\udc5c\ud835\udc60\ud835\udc56çã\ud835\udc5c) > \u2119(2 \ud835\udc56\ud835\udc54\ud835\udc62\ud835\udc4e\ud835\udc56\ud835\udc60 \ud835\udc60\ud835\udc52\ud835\udc5a \ud835\udc5f\ud835\udc52\ud835\udc5d\ud835\udc5c\ud835\udc60\ud835\udc56çã\ud835\udc5c) 
\ud835\udc5b2 +\ud835\udc5a2
(\ud835\udc5b +\ud835\udc5a)2
>
\ud835\udc5b(\ud835\udc5b \u2212 1) +\ud835\udc5a(\ud835\udc5a \u2212 1)
(\ud835\udc5b +\ud835\udc5a)(\ud835\udc5b +\ud835\udc5a \u2212 1)
 
\u21d2
(\ud835\udc5b2 +\ud835\udc5a2)
(\ud835\udc5b + \ud835\udc5a)(\ud835\udc5b + \ud835\udc5a)
\u2212
\ud835\udc5b(\ud835\udc5b \u2212 1) +\ud835\udc5a(\ud835\udc5a \u2212 1)
(\ud835\udc5b +\ud835\udc5a)(\ud835\udc5b +\ud835\udc5a \u2212 1)
> 0 
\u21d2
(\ud835\udc5b2 +\ud835\udc5a2)(\ud835\udc5b +\ud835\udc5a \u2212 1)
(\ud835\udc5b + \ud835\udc5a)(\ud835\udc5b + \ud835\udc5a)(\ud835\udc5b + \ud835\udc5a \u2212 1)
\u2212
(\ud835\udc5b(\ud835\udc5b \u2212 1) +\ud835\udc5a(\ud835\udc5a \u2212 1))(\ud835\udc5b + \ud835\udc5a)
(\ud835\udc5b + \ud835\udc5a)(\ud835\udc5b + \ud835\udc5a)(\ud835\udc5b +\ud835\udc5a \u2212 1)
> 0 
\u21d2 (\ud835\udc5b2 +\ud835\udc5a2)(\ud835\udc5b +\ud835\udc5a \u2212 1) \u2212 (\ud835\udc5b2 \u2212 \ud835\udc5b + \ud835\udc5a2 \u2212\ud835\udc5a)(\ud835\udc5b + \ud835\udc5a) > 0 
\u21d2 [(\ud835\udc5b3 + \ud835\udc5b2\ud835\udc5a \u2212 \ud835\udc5b2) + (\ud835\udc5b\ud835\udc5a2 +\ud835\udc5a3 \u2212\ud835\udc5a2)]
\u2212 [(\ud835\udc5b3 + \ud835\udc5b2\ud835\udc5a) \u2212 (\ud835\udc5b2 + \ud835\udc5b\ud835\udc5a) + (\ud835\udc5b\ud835\udc5a2 +\ud835\udc5a3) \u2212 (\ud835\udc5b\ud835\udc5a +\ud835\udc5a2)] > 0 
BC0406: Intr. à Prob. e à Estatística UFABC Resolução da Lista 03 v2 
 
 
Fernando Freitas Alves fernando.freitas@aluno.ufabc.edu.br 04/03/13 \u2013 pág. 6/11 
\u21d2 \u2212[\u2212\ud835\udc5b\ud835\udc5a \u2212 \ud835\udc5b\ud835\udc5a] > 0 
\u21d2 2\ud835\udc5b\ud835\udc5a > 0 
\u21d2 \ud835\udc5b\ud835\udc5a > 0 
\ud835\udc36\ud835\udc5c\ud835\udc5a\ud835\udc5c \ud835\udc5b > 0 \ud835\udc52 \ud835\udc5a > 0, \ud835\udc53\ud835\udc56\ud835\udc50\ud835\udc4e \ud835\udc5d\ud835\udc5f\ud835\udc5c\ud835\udc63\ud835\udc4e\ud835\udc51\ud835\udc5c \ud835\udc5c \ud835\udc52\ud835\udc65\ud835\udc52\ud835\udc5f\ud835\udc50í\ud835\udc50\ud835\udc56\ud835\udc5c.\u220e 
 
15. 
a) \u2119(\ud835\udc5f\ud835\udc52\ud835\udc60\ud835\udc5d\ud835\udc5c\ud835\udc5b\ud835\udc51\ud835\udc52\ud835\udc5f 5) = 
=
\u2115(\ud835\udc50\ud835\udc5c\ud835\udc5a\ud835\udc4f\ud835\udc56\ud835\udc5b\ud835\udc4eçõ\ud835\udc52\ud835\udc60 \ud835\udc51\ud835\udc52 \ud835\udc52\ud835\udc60\ud835\udc50\ud835\udc5c\ud835\udc59\u210e\ud835\udc52\ud835\udc5f 5 \ud835\udc51\ud835\udc5c\ud835\udc60 7 \ud835\udc5e\ud835\udc62\ud835\udc52 \ud835\udc60\ud835\udc4e\ud835\udc4f\ud835\udc52 \ud835\udc5f\ud835\udc52\ud835\udc60\ud835\udc5c\ud835\udc59\ud835\udc63\ud835\udc52\ud835\udc5f)
\u2115(\ud835\udc50\ud835\udc5c\ud835\udc5a\ud835\udc4f\ud835\udc56\ud835\udc5b\ud835\udc4eçõ\ud835\udc52\ud835\udc60 \ud835\udc51\ud835\udc52 \ud835\udc52\ud835\udc60\ud835\udc50\ud835\udc5c\ud835\udc59\u210e\ud835\udc52\ud835\udc5f 5 \ud835\udc51\ud835\udc5c\ud835\udc60 10 \ud835\udc61\ud835\udc5c\ud835\udc61\ud835\udc4e\ud835\udc56\ud835\udc60)
 
=
(7
5
)
(
10
5
)
 
=
7! 2!\u2044
10! 5!\u2044
 
=
\ud835\udfcf
\ud835\udfcf\ud835\udfd0
 
 
b) \u2119(\ud835\udc5d\ud835\udc52\ud835\udc59\ud835\udc5c \ud835\udc5a\ud835\udc52\ud835\udc5b\ud835\udc5c\ud835\udc60 4) = 
=
\u2115(\ud835\udc50\ud835\udc5c\ud835\udc5a\ud835\udc4f\ud835\udc56\ud835\udc5b\ud835\udc4eçõ\ud835\udc52\ud835\udc60 \ud835\udc51\ud835\udc52 \ud835\udc52\ud835\udc60\ud835\udc50\ud835\udc5c\ud835\udc59\u210e\ud835\udc52\ud835\udc5f 5 \ud835\udc51\ud835\udc5c\ud835\udc60 7 \ud835\udc5e\ud835\udc62\ud835\udc52 \ud835\udc60\ud835\udc4e\ud835\udc4f\ud835\udc52 \ud835\udc5f\ud835\udc52\ud835\udc60\ud835\udc5c\ud835\udc59\ud835\udc63\ud835\udc52\ud835\udc5f) + \u2115(\ud835\udc50\ud835\udc5c\ud835\udc5a\ud835\udc4f\ud835\udc56\ud835\udc5b\ud835\udc4eçõ\ud835\udc52\ud835\udc60 \ud835\udc51\ud835\udc52 \ud835\udc52\ud835\udc60\ud835\udc50\ud835\udc5c\ud835\udc59\u210e\ud835\udc52\ud835\udc5f 4 \ud835\udc51\ud835\udc5c\ud835\udc60 7)
\u2115(\ud835\udc50\ud835\udc5c\ud835\udc5a\ud835\udc4f\ud835\udc56\ud835\udc5b\ud835\udc4eçõ\ud835\udc52\ud835\udc60 \ud835\udc51\ud835\udc52 \ud835\udc52\ud835\udc60\ud835\udc50\ud835\udc5c\ud835\udc59\u210e\ud835\udc52\ud835\udc5f 5 \ud835\udc51\ud835\udc5c\ud835\udc60 10 \ud835\udc61\ud835\udc5c\ud835\udc61\ud835\udc4e\ud835\udc56\ud835\udc60)
 
=
(
7
5
) + (
7
4
) (10 \u2212 7
5 \u2212 4
)
(
10
5
)
 
=
\ud835\udfcf
\ud835\udfd0
 
 
16. 
\u2119(\ud835\udc3c\ud835\udc5b: {\ud835\udc5d\ud835\udc52\ud835\udc59\ud835\udc5c \ud835\udc5a\ud835\udc52\ud835\udc5b\ud835\udc5c\ud835\udc60 \ud835\udc51\ud835\udc5c\ud835\udc56\ud835\udc60 6 \ud835\udc4e\ud835\udc5d\ud835\udc4e\ud835\udc5f\ud835\udc52ç\ud835\udc4e\ud835\udc5a \ud835\udc5b\ud835\udc5c \ud835\udc5a\ud835\udc52\ud835\udc60\ud835\udc5a\ud835\udc5c \ud835\udc59\ud835\udc4e\ud835\udc5bç\ud835\udc4e\ud835\udc5a\ud835\udc52\ud835\udc5b\ud835\udc61\ud835\udc5c \ud835\udc5d/ \ud835\udc5b \ud835\udc59\ud835\udc4e\ud835\udc5bç\ud835\udc4e\ud835\udc5a\ud835\udc52\ud835\udc5b\ud835\udc61\ud835\udc5c\ud835\udc60}) = 
= 1\u2212 \u2119(\ud835\udc3c\ud835\udc5b
\ud835\udc36: {\ud835\udc5bã\ud835\udc5c \ud835\udc60\ud835\udc4e\ud835\udc56\ud835\udc5f \ud835\udc51\ud835\udc5c\ud835\udc56\ud835\udc60 6 \ud835\udc5b\ud835\udc5c \ud835\udc5a\ud835\udc52\ud835\udc60\ud835\udc5a\ud835\udc5c \ud835\udc59\ud835\udc4e\ud835\udc5bç\ud835\udc4e\ud835\udc5a\ud835\udc52\ud835\udc5b\ud835\udc61\ud835\udc5c \ud835\udc5d\ud835\udc4e\ud835\udc5f\ud835\udc4e \ud835\udc5b \ud835\udc59\ud835\udc4e\ud835\udc5bç\ud835\udc4e\ud835\udc5a\ud835\udc52\ud835\udc5b\ud835\udc61\ud835\udc5c\ud835\udc60}) 
= 1\u2212 (
36 \u2212 1
36
)
\ud835\udc5b
 
= 1\u2212 (
35
36
)
\ud835\udc5b
 
 
BC0406: Intr. à Prob. e à Estatística UFABC Resolução da Lista 03 v2 
 
 
Fernando Freitas Alves fernando.freitas@aluno.ufabc.edu.br 04/03/13 \u2013 pág. 7/11 
\u2119(\ud835\udc56\ud835\udc5b) \u2265
1
2
 
\u21d2 1 \u2212 (
35
36
)
\ud835\udc5b
\u2265
1
2
 
\u21d2 (
35
36
)
\ud835\udc5b
\u2264
1
2
 
\u21d2 log35
36
(
35
36
)
\ud835\udc5b
\u2265 log35
36
1
2
 
\u21d2 \ud835\udc5b \u2265 log35
36
1
2
 
\u21d2 \ud835\udc5b \u2265
ln
1
2
ln
35
36
 
\u21d2 \ud835\udc5b \u2265 24,61 
\u2234 \ud835\udc8f \u2265 \ud835\udfd0\ud835\udfd3 
 
17. 
a) \u2119(\ud835\udc4e) = 
=
\ud835\udfd0! (\ud835\udc75 \u2212 \ud835\udfcf)!
\ud835\udc75!
 
 
b) \u2119(\ud835\udc4f) = 
=
\u2119(\ud835\udc4e)
\ud835\udc41
 
=
\ud835\udfd0! (\ud835\udc75 \u2212 \ud835\udfcf)!
\ud835\udc75!\ud835\udc75
 
 
18.