# 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

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.```