Bioestatística — CE001
Prof. Fernando de Pol Mayer — Departamento de Estatística — DEST
Exercícios: probabilidade
Nome: GABARITO GRR:
1. Para cada um dos eventos abaixo, escreva o espaço amostral correspondente e conte seus elementos:
(a) Ω={CC,C R,RC,RR}n(Ω) = 4
(b) Ω={P P,P I ,I P,I I}n(Ω) = 4
(c) Ω={AA,AV,VA,V V }n(Ω) = 4
(d) Ω={2, 3, 4, . . . , 12}n(Ω) = 11
(e) Ω={MMM,MMF,MF M ,F M M ,FFM,FM F,M F F,FFF}n(Ω) = 8
(f) Ω={ω: 0 ≤ω≤20}n(Ω) = 21
(g) Ω={C,RC,RRC,RRRC,RRRRC, . . .}n(Ω) = ∞
(h) Ω={ω:ω > 0}=R+n(Ω) = ∞
(i) Ω={3, 4, 5, . . . , 10}n(Ω) = 8
(j) Ω={1, 2, 3, . . .}n(Ω) = ∞
(k) Ω={AA,AB,AC ,AD,AE ,BA,BB,BC ,B D,B E,C A,CB ,C C,C D,C E,DA,DB,DC ,DD,DE ,
EA,EB ,EC ,E D,E E }n(Ω) = 25
(l) Ω={AB,AC,AD,AE,BA,B C,BD,B E ,CA,C B,C D,C E ,DA,DB,DC,D E,E A,EB,EC ,E D}n(Ω) = 20
(m) Ω={AB,AC,AD,AE,B C,BD,BE ,C D,C E ,DE}n(Ω) = 10
2. Ω={BC ,BR,V B,V V }
3. (a) Ω={V V,VA,V B,AA,AV,AB,BB,BA,BV }
(b) Ω={VA,V B,AV,AB,BA,BV }
4. (a) Ω={x:x>0}
(b) A∪B={x:x>11}
(c) A∩B={x: 11 <x≤15}
(d) Ac={x:x≤11}
(e) A∪B∪C={x:x≥8}
(f) (A∪C)c={x:x<8}
(g) A∩B∩C=∅
(h) Bc∩C=∅
(i) A∪(B∩C) = {x:x≥8}
5. Ω={ω:ω≥0}
(a) A={ω: 675 ≤ω≤700}
(b) B={ω: 450 ≤ω≤500}
(c) A∩B=∅
(d) A∪B={ω: 450 ≤ω≤500 ∪675 ≤ω≤700}
6. Ω={PPP,P P N,P N P,N P P,P N N ,N P N,N N P,NNN}
(a) A={PPP}
(b) B={NNN}
(c) A∩B=∅
(d) A∪B={PPP,NNN}
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