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# Resolução lista 04 IPE

DisciplinaIntrodução à Probabilidade e A Estatística II218 materiais1.684 seguidores
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```BC0406: Intr. à Prob. e à Estatística UFABC Resolução da Lista 04 v1

Fernando Freitas Alves fernando.freitas@aluno.ufabc.edu.br 02/03/13 \u2013 pág. 1/19
1.
\ud835\udc38\ud835\udc63\ud835\udc52\ud835\udc5b\ud835\udc61\ud835\udc5c\ud835\udc60:
\ud835\udc46\ud835\udc56: {\ud835\udc60\ud835\udc5c\ud835\udc5a\ud835\udc4e \ud835\udc51\ud835\udc5c\ud835\udc60 \ud835\udc51\ud835\udc5c\ud835\udc56\ud835\udc60 \ud835\udc51\ud835\udc4e\ud835\udc51\ud835\udc5c\ud835\udc60 \ud835\udc51á \ud835\udc56}
\ud835\udc39: {\ud835\udc51\ud835\udc4e\ud835\udc51\ud835\udc5c\ud835\udc60 \ud835\udc50\ud835\udc4eí\ud835\udc5f\ud835\udc4e\ud835\udc5a \ud835\udc50\ud835\udc5c\ud835\udc5a \ud835\udc5c\ud835\udc60 \ud835\udc5bú\ud835\udc5a\ud835\udc52\ud835\udc5f\ud835\udc5c\ud835\udc60 \ud835\udc51\ud835\udc4e\ud835\udc60 \ud835\udc53\ud835\udc4e\ud835\udc50\ud835\udc52\ud835\udc60 \ud835\udc51\ud835\udc56\ud835\udc53\ud835\udc52\ud835\udc5f\ud835\udc52\ud835\udc5b\ud835\udc61\ud835\udc52\ud835\udc60}
\ud835\udc3c: {\ud835\udc51\ud835\udc4e\ud835\udc51\ud835\udc5c\ud835\udc60 \ud835\udc50\ud835\udc4eí\ud835\udc5f\ud835\udc4e\ud835\udc5a \ud835\udc50\ud835\udc5c\ud835\udc5a \ud835\udc5c\ud835\udc60 \ud835\udc5bú\ud835\udc5a\ud835\udc52\ud835\udc5f\ud835\udc5c\ud835\udc60 \ud835\udc51\ud835\udc4e\ud835\udc60 \ud835\udc53\ud835\udc4e\ud835\udc50\ud835\udc52\ud835\udc60 \ud835\udc56\ud835\udc54\ud835\udc62\ud835\udc4e\ud835\udc56\ud835\udc60}
2\ud835\udc37\ud835\udc56: {\ud835\udc60\ud835\udc52\ud835\udc54\ud835\udc62\ud835\udc5b\ud835\udc51\ud835\udc5c \ud835\udc51\ud835\udc4e\ud835\udc51\ud835\udc5c \ud835\udc50\ud835\udc5c\ud835\udc5a \ud835\udc5f\ud835\udc52\ud835\udc60\ud835\udc62\ud835\udc59\ud835\udc61\ud835\udc4e\ud835\udc51\ud835\udc5c \ud835\udc56}

a) \u2119(\ud835\udc466|\ud835\udc39) =
=
\u2119(\ud835\udc466 \u2229 \ud835\udc39)
\u2119(\ud835\udc39)

=
\u2119(\ud835\udc466 \u2229 \ud835\udc39)
1 \u2212 \u2119(\ud835\udc3c)

=
(
2! (1
1
) (5
1
)
62
)
1 \u2212 (
6
62
)

=
\ud835\udfcf
\ud835\udfd1

b) \u2119(2\ud835\udc376|\ud835\udc462) = \ud835\udfce
\u2119(2\ud835\udc376|\ud835\udc463) = \ud835\udfce
\u2119(2\ud835\udc376|\ud835\udc464) = \ud835\udfce
\u2119(2\ud835\udc376|\ud835\udc465) = \ud835\udfce
\u2119(2\ud835\udc376|\ud835\udc466) = \ud835\udfce
\u2119(2\ud835\udc376|\ud835\udc467) =
\ud835\udfcf
\ud835\udfd4

\u2119(2\ud835\udc376|\ud835\udc468) =
\ud835\udfcf
\ud835\udfd3

\u2119(2\ud835\udc376|\ud835\udc469) =
\ud835\udfcf
\ud835\udfd2

\u2119(2\ud835\udc376|\ud835\udc4610) =
\ud835\udfcf
\ud835\udfd1

\u2119(2\ud835\udc376|\ud835\udc4611) =
\ud835\udfcf
\ud835\udfd0

BC0406: Intr. à Prob. e à Estatística UFABC Resolução da Lista 04 v1

Fernando Freitas Alves fernando.freitas@aluno.ufabc.edu.br 02/03/13 \u2013 pág. 2/19
\u2119(2\ud835\udc376|\ud835\udc4612) = \ud835\udfcf

2.
\ud835\udc38\ud835\udc63\ud835\udc52\ud835\udc5b\ud835\udc61\ud835\udc5c\ud835\udc60:
\ud835\udc35: {\ud835\udc4f\ud835\udc5c\ud835\udc59\ud835\udc4e\ud835\udc60 \ud835\udc4f\ud835\udc5f\ud835\udc4e\ud835\udc5b\ud835\udc50\ud835\udc4e}
\ud835\udc41: {\ud835\udc4f\ud835\udc5c\ud835\udc59\ud835\udc4e \ud835\udc5b\ud835\udc52\ud835\udc54\ud835\udc5f\ud835\udc4e}
\ud835\udc56\ud835\udc35: \ud835\udc5e\ud835\udc62\ud835\udc4e\ud835\udc5b\ud835\udc61\ud835\udc56\ud835\udc51\ud835\udc4e\ud835\udc51\ud835\udc52 \ud835\udc51\ud835\udc52 \ud835\udc4f\ud835\udc5c\ud835\udc59\ud835\udc4e\ud835\udc60 \ud835\udc4f\ud835\udc5f\ud835\udc4e\ud835\udc5b\ud835\udc50\ud835\udc4e\ud835\udc60 \ud835\udc61\ud835\udc56\ud835\udc5f\ud835\udc4e\ud835\udc51\ud835\udc4e\ud835\udc60 \ud835\udc4e\ud835\udc61é \ud835\udc56
\ud835\udc56\ud835\udc41: \ud835\udc5e\ud835\udc62\ud835\udc4e\ud835\udc5b\ud835\udc61\ud835\udc56\ud835\udc51\ud835\udc4e\ud835\udc51\ud835\udc52 \ud835\udc51\ud835\udc52 \ud835\udc4f\ud835\udc5c\ud835\udc59\ud835\udc4e\ud835\udc60 \ud835\udc5b\ud835\udc52\ud835\udc54\ud835\udc5f\ud835\udc4e\ud835\udc60 \ud835\udc61\ud835\udc56\ud835\udc5f\ud835\udc4e\ud835\udc51\ud835\udc4e\ud835\udc60 \ud835\udc4e\ud835\udc61é \ud835\udc56

\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc5a\ud835\udc56\ud835\udc60\ud835\udc60\ud835\udc4e\ud835\udc60:
\u2119(\ud835\udc35\ud835\udc56) =
6 \u2212 (\ud835\udc56\ud835\udc35 \u2212 1)
6 + 9 \u2212 (\ud835\udc56 \u2212 1)
=
6
15

\u2119(\ud835\udc41\ud835\udc56) =
9 \u2212 (\ud835\udc56\ud835\udc41 \u2212 1)
6 + 9 \u2212 (\ud835\udc56 \u2212 1)
=
9
15

\u2119({\ud835\udc35, \ud835\udc35, \ud835\udc41, \ud835\udc41}) =
= \u2119(\ud835\udc351 \u2229 \ud835\udc352 \u2229 \ud835\udc413 \u2229 \ud835\udc414)
= (
6
15
) (
6 \u2212 1
15 \u2212 1
) (
9
15 \u2212 2
) (
9 \u2212 1
15 \u2212 3
)
=
\ud835\udfd4
\ud835\udfd7\ud835\udfcf

3.
\ud835\udc38\ud835\udc63\ud835\udc52\ud835\udc5b\ud835\udc61\ud835\udc5c\ud835\udc60:
3\ud835\udc35: {3 \ud835\udc4f\ud835\udc5c\ud835\udc59\ud835\udc4e\ud835\udc60 \ud835\udc4f\ud835\udc5f\ud835\udc4e\ud835\udc5b\ud835\udc50\ud835\udc4e\ud835\udc60}
\ud835\udc35\ud835\udc56: {\ud835\udc56é\ud835\udc60\ud835\udc56\ud835\udc5a\ud835\udc4e \ud835\udc4f\ud835\udc5c\ud835\udc59\ud835\udc4e \ud835\udc4f\ud835\udc5f\ud835\udc4e\ud835\udc5b\ud835\udc50\ud835\udc4e}
\ud835\udc35\ufffd\u305\ufffd: {\ud835\udc56é\ud835\udc60\ud835\udc56\ud835\udc5a\ud835\udc4e \ud835\udc4f\ud835\udc5c\ud835\udc59\ud835\udc4e \ud835\udc5bã\ud835\udc5c \ud835\udc4f\ud835\udc5f\ud835\udc4e\ud835\udc5b\ud835\udc50\ud835\udc4e}

\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc5a\ud835\udc56\ud835\udc60\ud835\udc60\ud835\udc4e\ud835\udc60:
\uf0b7 \ud835\udc36\ud835\udc5c\ud835\udc5a \ud835\udc5f\ud835\udc52\ud835\udc5d\ud835\udc5c\ud835\udc60\ud835\udc56çã\ud835\udc5c:
\u2119(\ud835\udc35\ud835\udc56) = \u2119(\ud835\udc35) =
8
12

BC0406: Intr. à Prob. e à Estatística UFABC Resolução da Lista 04 v1

Fernando Freitas Alves fernando.freitas@aluno.ufabc.edu.br 02/03/13 \u2013 pág. 3/19
\u2119(\ud835\udc35\ufffd\u305\ufffd) = \u2119(\ufffd\u305\ufffd) =
12 \u2212 8
12
=
4
12

\uf0b7 \ud835\udc46\ud835\udc52\ud835\udc5a \ud835\udc5f\ud835\udc52\ud835\udc5d\ud835\udc5c\ud835\udc60\ud835\udc56çã\ud835\udc5c:
\u2119 (\ud835\udc35\ud835\udc56 | \u22c2 \ud835\udc35\ud835\udc57
\ud835\udc5b
\ud835\udc57
\u22c2 \ud835\udc35\ud835\udc58
\ud835\udc5a
\ud835\udc58
) =
8 \u2212 \ud835\udc5b
12 \u2212 (\ud835\udc56 \u2212 1)
; \ud835\udc5b + \ud835\udc5a = \ud835\udc56 \u2212 1
\u2119 (\ud835\udc35\ud835\udc56 | \u22c2 \ud835\udc35\ud835\udc57
\ud835\udc5b
\ud835\udc57
\u22c2 \ud835\udc35\ud835\udc58
\ud835\udc5a
\ud835\udc58
) =
(12 \u2212 8) \u2212 \ud835\udc5a
12 \u2212 (\ud835\udc56 \u2212 1)
=
4 \u2212 \ud835\udc5a
12 \u2212 (\ud835\udc56 \u2212 1)
; \ud835\udc5b + \ud835\udc5a = \ud835\udc56 \u2212 1

\u2119(\ud835\udc351 \u2229 \ud835\udc353|3\ud835\udc4f) =
=
\u2119(\ud835\udc351 \u2229 \ud835\udc353 \u2229 3\ud835\udc4f)
\u2119(3\ud835\udc4f)

=
\u2119 (\ud835\udc351 \u2229 \ud835\udc353 \u2229 ((\ud835\udc351 \u2229 \ud835\udc352 \u2229 \ud835\udc353 \u2229 \ud835\udc354\u305\u305 \u305) \u222a (\ud835\udc351 \u2229 \ud835\udc352 \u2229 \ud835\udc353\u305\u305 \u305 \u2229 \ud835\udc354) \u222a (\ud835\udc351 \u2229 \ud835\udc352\u305\u305 \u305 \u2229 \ud835\udc353 \u2229 \ud835\udc354) \u222a (\ud835\udc351\u305\u305 \u305 \u2229 \ud835\udc352 \u2229 \ud835\udc353 \u2229 \ud835\udc354)))
\u2119((\ud835\udc351 \u2229 \ud835\udc352 \u2229 \ud835\udc353 \u2229 \ud835\udc354\u305\u305 \u305) \u222a (\ud835\udc351 \u2229 \ud835\udc352 \u2229 \ud835\udc353\u305\u305 \u305 \u2229 \ud835\udc354) \u222a (\ud835\udc351 \u2229 \ud835\udc352\u305\u305 \u305 \u2229 \ud835\udc353 \u2229 \ud835\udc354) \u222a (\ud835\udc351\u305\u305 \u305 \u2229 \ud835\udc352 \u2229 \ud835\udc353 \u2229 \ud835\udc354))

=
\u2119((\ud835\udc351 \u2229 \ud835\udc352 \u2229 \ud835\udc353 \u2229 \ud835\udc354\u305\u305 \u305) \u222a (\ud835\udc351 \u2229 \ud835\udc352\u305\u305 \u305 \u2229 \ud835\udc353 \u2229 \ud835\udc354))
\u2119((\ud835\udc351 \u2229 \ud835\udc352 \u2229 \ud835\udc353 \u2229 \ud835\udc354\u305\u305 \u305) \u222a (\ud835\udc351 \u2229 \ud835\udc352 \u2229 \ud835\udc353\u305\u305 \u305 \u2229 \ud835\udc354) \u222a (\ud835\udc351 \u2229 \ud835\udc352\u305\u305 \u305 \u2229 \ud835\udc353 \u2229 \ud835\udc354) \u222a (\ud835\udc351\u305\u305 \u305 \u2229 \ud835\udc352 \u2229 \ud835\udc353 \u2229 \ud835\udc354))

=
\u2119(\ud835\udc351 \u2229 \ud835\udc352 \u2229 \ud835\udc353 \u2229 \ud835\udc354\u305\u305 \u305) + \u2119(\ud835\udc351 \u2229 \ud835\udc352\u305\u305 \u305 \u2229 \ud835\udc353 \u2229 \ud835\udc354)
\u2119(\ud835\udc351 \u2229 \ud835\udc352 \u2229 \ud835\udc353 \u2229 \ud835\udc354\u305\u305 \u305) + \u2119(\ud835\udc351 \u2229 \ud835\udc352 \u2229 \ud835\udc353\u305\u305 \u305 \u2229 \ud835\udc354) + \u2119(\ud835\udc351 \u2229 \ud835\udc352\u305\u305 \u305 \u2229 \ud835\udc353 \u2229 \ud835\udc354) + \u2119(\ud835\udc351\u305\u305 \u305 \u2229 \ud835\udc352 \u2229 \ud835\udc353 \u2229 \ud835\udc354)

=
1
1 +
\u2119(\ud835\udc351 \u2229 \ud835\udc352 \u2229 \ud835\udc353\u305\u305 \u305 \u2229 \ud835\udc354) + \u2119(\ud835\udc351\u305\u305 \u305 \u2229 \ud835\udc352 \u2229 \ud835\udc353 \u2229 \ud835\udc354)
\u2119(\ud835\udc351 \u2229 \ud835\udc352 \u2229 \ud835\udc353 \u2229 \ud835\udc354\u305\u305 \u305) + \u2119(\ud835\udc351 \u2229 \ud835\udc352\u305\u305 \u305 \u2229 \ud835\udc353 \u2229 \ud835\udc354)

\uf0b7 \ud835\udc36\ud835\udc5c\ud835\udc5a \ud835\udc5f\ud835\udc52\ud835\udc5d\ud835\udc5c\ud835\udc60\ud835\udc56çã\ud835\udc5c:
=
1
1 +
\u2119(\ud835\udc351) · \u2119(\ud835\udc352) · \u2119(\ud835\udc353\u305\u305 \u305) · \u2119(\ud835\udc354) + \u2119(\ud835\udc351\u305\u305 \u305) · \u2119(\ud835\udc352) · \u2119(\ud835\udc353) · \u2119(\ud835\udc354)
\u2119(\ud835\udc351) · \u2119(\ud835\udc352) · \u2119(\ud835\udc353) · \u2119(\ud835\udc354\u305\u305 \u305) + \u2119(\ud835\udc351) · \u2119(\ud835\udc352\u305\u305 \u305) · \u2119(\ud835\udc353) · \u2119(\ud835\udc354)

=
1
1 +
(
\u2119(\ud835\udc353\u305\u305 \u305)
\u2119(\ud835\udc353)
+
\u2119(\ud835\udc351\u305\u305 \u305)
\u2119(\ud835\udc351)
)
(
\u2119(\ud835\udc354\u305\u305 \u305)
\u2119(\ud835\udc354)
+
\u2119(\ud835\udc352\u305\u305 \u305)
\u2119(\ud835\udc352)
)

=
1
1 +
(
\u2119(\ufffd\u305\ufffd)
\u2119(\ud835\udc35)
+
\u2119(\ufffd\u305\ufffd)
\u2119(\ud835\udc35)
)
(
\u2119(\ufffd\u305\ufffd)
\u2119(\ud835\udc35)
+
\u2119(\ufffd\u305\ufffd)
\u2119(\ud835\udc35)
)

=
\ud835\udfcf
\ud835\udfd0

BC0406: Intr. à Prob. e à Estatística UFABC Resolução da Lista 04 v1

Fernando Freitas Alves fernando.freitas@aluno.ufabc.edu.br 02/03/13 \u2013 pág. 4/19
\uf0b7 \ud835\udc46\ud835\udc52\ud835\udc5a \ud835\udc5f\ud835\udc52\ud835\udc5d\ud835\udc5c\ud835\udc60\ud835\udc56çã\ud835\udc5c:
=
1
1 +
\u2119(\ud835\udc351 \u2229 \ud835\udc352 \u2229 \ud835\udc353\u305\u305 \u305 \u2229 \ud835\udc354) + \u2119(\ud835\udc351\u305\u305 \u305 \u2229 \ud835\udc352 \u2229 \ud835\udc353 \u2229 \ud835\udc354)
\u2119(\ud835\udc351 \u2229 \ud835\udc352 \u2229 \ud835\udc353 \u2229 \ud835\udc354\u305\u305 \u305) + \u2119(\ud835\udc351 \u2229 \ud835\udc352\u305\u305 \u305 \u2229 \ud835\udc353 \u2229 \ud835\udc354)

=
1
1 +
\u2119(\ud835\udc351)\u2119(\ud835\udc352|\ud835\udc351)\u2119(\ud835\udc353\u305\u305 \u305|\ud835\udc351 \u2229 \ud835\udc352)\u2119(\ud835\udc354|\ud835\udc351 \u2229 \ud835\udc352 \u2229 \ud835\udc353\u305\u305 \u305) + \u2119(\ud835\udc351)\u2119(\ud835\udc352|\ud835\udc351)\u2119(\ud835\udc353|\ud835\udc351 \u2229 \ud835\udc352)\u2119(\ud835\udc354|\ud835\udc351 \u2229 \ud835\udc352 \u2229 \ud835\udc353)
\u2119(\ud835\udc351)\u2119(\ud835\udc352|\ud835\udc351)\u2119(\ud835\udc353|\ud835\udc351 \u2229 \ud835\udc352)\u2119(\ud835\udc354|\ud835\udc351 \u2229 \ud835\udc352 \u2229 \ud835\udc353) + \u2119(\ud835\udc351)\u2119(\ud835\udc352|\ud835\udc351)\u2119(\ud835\udc353|\ud835\udc351 \u2229 \ud835\udc352)\u2119(\ud835\udc354|\ud835\udc351 \u2229 \ud835\udc352 \u2229 \ud835\udc353)

=
1
1 +
(
8
12 ×
8 \u2212 1
12 \u2212 1 ×
4
12 \u2212 2 ×
8 \u2212 2
12 \u2212 3
) + (
4
12 ×
8
12 \u2212 1 ×
8 \u2212 1
12 \u2212 2 ×
8 \u2212 2
12 \u2212 3
)
(
8
12 ×
8 \u2212 1
12 \u2212 1 ×
8 \u2212 2
12 \u2212 2 ×
4
12 \u2212 3
) + (
8
12 ×
4
12 \u2212 1 ×
8 \u2212 1
12 \u2212 2 ×
8 \u2212 2
12 \u2212 3
)

=
1
1 +
(8 × 7 × 4 × 6) + (4 × 8 × 7 × 6)
(8 × 7 × 6 × 4) + (8 × 4 × 7 × 6)

=
\ud835\udfcf
\ud835\udfd0

4.
\ud835\udc38\ud835\udc63\ud835\udc52\ud835\udc5b\ud835\udc61\ud835\udc5c\ud835\udc60:
2\ud835\udc53: {2 \ud835\udc5a\ud835\udc52\ud835\udc5b\ud835\udc56\ud835\udc5b\ud835\udc4e\ud835\udc60}
\ud835\udc40\ud835\udc53: {\ud835\udc5a\ud835\udc4e\ud835\udc56\ud835\udc60 \ud835\udc63\ud835\udc52\ud835\udc59\u210e\ud835\udc4e\ud835\udc60 \ud835\udc5a\ud835\udc52\ud835\udc5b\ud835\udc56\ud835\udc5b\ud835\udc4e}
\ud835\udc5a\ud835\udc53: {\ud835\udc5a\ud835\udc4e\ud835\udc56\ud835\udc60 \ud835\udc5b\ud835\udc5c\ud835\udc63\ud835\udc4e \ud835\udc5a\ud835\udc52\ud835\udc5b\ud835\udc56\ud835\udc5b\ud835\udc4e}

\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc5a\ud835\udc56\ud835\udc60\ud835\udc60\ud835\udc4e\ud835\udc60:
\ud835\udc43(\ud835\udc40\ud835\udc53) = \ud835\udc43(\ud835\udc5a\ud835\udc53) =
1
2

\ud835\udc43(2\ud835\udc53) = \ud835\udc43(\ud835\udc40\ud835\udc53 \u2229 \ud835\udc5a\ud835\udc53) = \ud835\udc43(\ud835\udc40\ud835\udc53) · \ud835\udc43(\ud835\udc5a\ud835\udc53) =
1
4

\u2119(2\ud835\udc53|\ud835\udc40\ud835\udc53) =
=
\u2119(2\ud835\udc53 \u2229 \ud835\udc40\ud835\udc53)
\u2119(\ud835\udc40\ud835\udc53)

=
\u2119 ((\ud835\udc40\ud835\udc53 \u2229 \ud835\udc5a\ud835\udc53) \u2229 \ud835\udc40\ud835\udc53)
\u2119(\ud835\udc40\ud835\udc53)

=
\u2119(\ud835\udc40\ud835\udc53 \u2229 \ud835\udc5a\ud835\udc53)
\u2119(\ud835\udc40\ud835\udc53)

BC0406: Intr. à Prob. e à Estatística UFABC Resolução da Lista 04 v1

Fernando Freitas Alves fernando.freitas@aluno.ufabc.edu.br 02/03/13 \u2013 pág. 5/19
=
\u2119(2\ud835\udc53)
\u2119(\ud835\udc40\ud835\udc53)

=
1
4\u2044
1
2\u2044

=
\ud835\udfcf
\ud835\udfd0

5.
\ud835\udc38\ud835\udc63\ud835\udc52\ud835\udc5b\ud835\udc61\ud835\udc5c\ud835\udc60:
2\ud835\udc4f: {2 \ud835\udc4f\ud835\udc5c\ud835\udc59\ud835\udc4e\ud835\udc60 \ud835\udc4f\ud835\udc5f\ud835\udc4e\ud835\udc5b\ud835\udc50\ud835\udc4e\ud835\udc60}
\ud835\udc4b\ud835\udc4f: {\ud835\udc4f\ud835\udc5c\ud835\udc59\ud835\udc4e \ud835\udc4f\ud835\udc5f\ud835\udc4e\ud835\udc5b\ud835\udc50\ud835\udc4e \ud835\udc5b\ud835\udc4e \ud835\udc62\ud835\udc5f\ud835\udc5b\ud835\udc4e \ud835\udc4b}
\ud835\udc4b\ud835\udc63: {\ud835\udc4f\ud835\udc5c\ud835\udc59\ud835\udc4e \ud835\udc63\ud835\udc52\ud835\udc5f\ud835\udc5a\ud835\udc52\ud835\udc59\u210e\ud835\udc4e \ud835\udc5b\ud835\udc4e \ud835\udc62\ud835\udc5f\ud835\udc5b\ud835\udc4e \ud835\udc4b}

\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc5a\ud835\udc56\ud835\udc60\ud835\udc60\ud835\udc4e\ud835\udc60:
\u2119(\ud835\udc34\ud835\udc4f) =
2
2 + 4
=
1
3

\u2119(\ud835\udc35\ud835\udc4f) =
8
8 + 4
=
2
3

\u2119(\ud835\udc36\ud835\udc4f) =
1
1 + 3
=
1
4

\u2119(\ud835\udc34\ud835\udc63) =
4
2 + 4
=
2
3

\u2119(\ud835\udc35\ud835\udc63) =
4
8 + 4
=
1
3

\u2119(\ud835\udc36\ud835\udc63) =
3
1 + 3
=
3
4

\u2119(\ud835\udc34\ud835\udc4f|2\ud835\udc4f) =
=
\u2119(\ud835\udc34\ud835\udc4f \u2229 2\ud835\udc4f)
\u2119(2\ud835\udc4f)

=
\u2119 (\ud835\udc34\ud835\udc4f \u2229 ((\ud835\udc34\ud835\udc4f \u2229 \ud835\udc35\ud835\udc4f \u2229 \ud835\udc36\ud835\udc63) \u222a (\ud835\udc34\ud835\udc4f \u2229 \ud835\udc35\ud835\udc63 \u2229 \ud835\udc36\ud835\udc4f) \u222a (\ud835\udc34\ud835\udc63 \u2229 \ud835\udc35\ud835\udc4f \u2229 \ud835\udc36\ud835\udc4f)))
\u2119((\ud835\udc34\ud835\udc4f \u2229 \ud835\udc35\ud835\udc4f \u2229 \ud835\udc36\ud835\udc63) \u222a (\ud835\udc34\ud835\udc4f \u2229 \ud835\udc35\ud835\udc63 \u2229 \ud835\udc36\ud835\udc4f) \u222a (\ud835\udc34\ud835\udc63 \u2229 \ud835\udc35\ud835\udc4f \u2229 \ud835\udc36\ud835\udc4f))

=
\u2119((\ud835\udc34\ud835\udc4f \u2229 \ud835\udc35\ud835\udc4f \u2229 \ud835\udc36\ud835\udc63) \u222a (\ud835\udc34\ud835\udc4f \u2229 \ud835\udc35\ud835\udc63 \u2229 \ud835\udc36\ud835\udc4f))
\u2119((\ud835\udc34\ud835\udc4f \u2229 \ud835\udc35\ud835\udc4f \u2229 \ud835\udc36\ud835\udc63) \u222a (\ud835\udc34\ud835\udc4f \u2229 \ud835\udc35\ud835\udc63 \u2229 \ud835\udc36\ud835\udc4f) \u222a (\ud835\udc34\ud835\udc63 \u2229 \ud835\udc35\ud835\udc4f \u2229 \ud835\udc36\ud835\udc4f))

BC0406: Intr. à Prob. e à Estatística UFABC Resolução da Lista 04 v1

Fernando Freitas Alves fernando.freitas@aluno.ufabc.edu.br 02/03/13 \u2013 pág. 6/19
=
\u2119(\ud835\udc34\ud835\udc4f \u2229 \ud835\udc35\ud835\udc4f \u2229 \ud835\udc36\ud835\udc63 ) + \u2119(\ud835\udc34\ud835\udc4f \u2229 \ud835\udc35\ud835\udc63 \u2229 \ud835\udc36\ud835\udc4f)
\u2119(\ud835\udc34\ud835\udc4f \u2229 \ud835\udc35\ud835\udc4f \u2229 \ud835\udc36\ud835\udc63) + \u2119(\ud835\udc34\ud835\udc4f \u2229 \ud835\udc35\ud835\udc63 \u2229 \ud835\udc36\ud835\udc4f) + \u2119(\ud835\udc34\ud835\udc63 \u2229 \ud835\udc35\ud835\udc4f \u2229 \ud835\udc36\ud835\udc4f)

=
1
1 +
\u2119(\ud835\udc34\ud835\udc63 \u2229 \ud835\udc35\ud835\udc4f \u2229 \ud835\udc36\ud835\udc4f)
\u2119(\ud835\udc34\ud835\udc4f \u2229 \ud835\udc35\ud835\udc4f \u2229 \ud835\udc36\ud835\udc63) + \u2119(\ud835\udc34\ud835\udc4f \u2229 \ud835\udc35\ud835\udc63 \u2229 \ud835\udc36\ud835\udc4f)

=
1
1 +
\u2119(\ud835\udc34\ud835\udc63) · \u2119(\ud835\udc35\ud835\udc4f) · \u2119(\ud835\udc36\ud835\udc4f)
\u2119(\ud835\udc34\ud835\udc4f) · \u2119(\ud835\udc35\ud835\udc4f) · \u2119(\ud835\udc36\ud835\udc63) + \u2119(\ud835\udc34\ud835\udc4f) · \u2119(\ud835\udc35\ud835\udc63) · \u2119(\ud835\udc36\ud835\udc4f)

=
1
1 +
\u2119(\ud835\udc34\ud835\udc63)
\u2119(\ud835\udc34\ud835\udc4f)
\u2119(\ud835\udc36\ud835\udc63)
\u2119(\ud835\udc36\ud835\udc4f)
+
\u2119(\ud835\udc35\ud835\udc63)
\u2119(\ud835\udc35\ud835\udc4f)

=
1
1 +
2/3
1 3\u2044
3 4\u2044
1 4\u2044
+
1 3\u2044
2 3\u2044

=
1
1 +
2
3 +
1
2

=
1
1 +
4
7

=
\ud835\udfd5
\ud835\udfcf\ud835\udfcf

6.
\ud835\udc38\ud835\udc63\ud835\udc52\ud835\udc5b\ud835\udc61\ud835\udc5c\ud835\udc60:
\ud835\udc46: {\ud835\udc56é\ud835\udc60\ud835\udc56\ud835\udc5a\ud835\udc4e \ud835\udc50\ud835\udc4e\ud835\udc5f\ud835\udc61\ud835\udc4e \ud835\udc5f\ud835\udc52\ud835\udc61\ud835\udc56\ud835\udc5f\ud835\udc4e\ud835\udc51\ud835\udc4e é \ud835\udc51\ud835\udc52 \ud835\udc52\ud835\udc60\ud835\udc5d\ud835\udc4e\ud835\udc51\ud835\udc4e\ud835\udc60}

\ud835\udc43\ud835\udc5f\ud835\udc52\ud835\udc5a\ud835\udc56\ud835\udc60\ud835\udc60\ud835\udc4e\ud835\udc60:
\u2119(\ud835\udc46\ud835\udc56) =
(13
1
)
(52
1
)

\u2119(\ud835\udc46\ud835\udc56| \u22c3 \ud835\udc46\ud835\udc57
\ud835\udc5b
\ud835\udc57 ) =
(13 \u2212
(\ud835\udc5b \u2212 \ud835\udc57 + 1)
1
)
(52 \u2212
(\ud835\udc5b \u2212 \ud835\udc57 + 1)
1
)

BC0406: Intr. à Prob. e à Estatística UFABC Resolução da Lista 04 v1

Fernando Freitas Alves fernando.freitas@aluno.ufabc.edu.br 02/03/13 \u2013 pág. 7/19
\u2119(\ud835\udc461|\ud835\udc462 \u2229 \ud835\udc463) =
=
\u2119(\ud835\udc461 \u2229 \ud835\udc462 \u2229 \ud835\udc463)
\u2119(\ud835\udc463 \u2229 \ud835\udc462)

=
\u2119(\ud835\udc461) · \u2119(\ud835\udc462|\ud835\udc461) · \u2119(\ud835\udc463|\ud835\udc461 \u2229 \ud835\udc462)
\u2119(\ud835\udc463|\ud835\udc462) · \u2119(\ud835\udc462)

=
\u2119(\ud835\udc462|\ud835\udc461) · \u2119(\ud835\udc463|\ud835\udc461 \u2229 \ud835\udc462)
\u2119(\ud835\udc463|\ud835\udc462)

=
(13 \u2212
(1 \u2212 1 + 1)
1
)
(52 \u2212
(1 \u2212 1 + 1)
1
)
·
(13 \u2212
(2 \u2212 1 + 1)
1
)
(52 \u2212
(2 \u2212 1 + 1)
1
)
(13 \u2212
(1 \u2212 1 + 1)
1
)
(52 \u2212
(1 \u2212 1 + 1)
1
)

=
\ud835\udfcf\ud835\udfcf
\ud835\udfd3\ud835\udfce

7.
\ud835\udc38\ud835\udc63\ud835\udc52\ud835\udc5b\ud835\udc61\ud835\udc5c\ud835\udc60:
\ud835\udc35: {2 \ud835\udc4e\ud835\udc60\ud835\udc52\ud835\udc60}
\ud835\udc34\ud835\udc46: {1 á\ud835\udc60 \ud835\udc51\ud835\udc52 \ud835\udc52\ud835\udc60\ud835\udc5d\ud835\udc4e\ud835\udc51\ud835\udc4e\ud835\udc60}
\ud835\udc34:```