Respostas Capitulo 3 Modelos Probabilisticos

Capítulo 3

Modelos Probabilísticos

Respostas aos Exercícios Propostos

1) 3
P( X = 3 ) = C .(1/2)3 (1/2)2 = 0,3125 ou 31,25%. 5

2)

0 1 2
P( X ≤ 2 ) = C .(1/6)0 (5/6)3 + C .(1/6)0 (5/6)3 + C .(1/6)2 (5/6)1 = 0,9950 ou 99,50%. 3 3 3

3) 4 5
P( X ≥ 4 ) = C .(2/3)4 (1/3)1 + C .(2/3)5 (1/3)0 = 0,4608 ou 46,08%. 5 5

4) 3
P( X = 3 ) = C .(1/3)3 (2/3)2 = 0,1646 ou 16,46%. 5

5)

3
P( X = 3 ) = C .(0,70)3 (0,30)3 = 0,1852 ou 18,52%. 6

6)

10
P( X = 10 ) = C .(1/3)10 (2/3)20 = 0,1530 ou 15,30%. 30 0
P( X = 0 ) = C .(1/3)0 (2/3)30 = 0,0000 ou 00,00%. 30 1 2 3 4
P( X ≤ 4 ) = C .(1/3)1 (2/3)29 + C (1/3)2(2/3)28 + C (1/3)3(2/3)27 + C (1/3)4(2/3)26 = 30 30 30 30
P( X ≤ 4 ) = 0,012 ou 1,20%

P( X ≥ 5) = 1 – P( X ≤ 4 ) = 1 – 0,012 = 0,9880 ou 98,80%

E( 5X ) = 5 E( X ) = 5 . 30 .(1/3) =R$ 50,00

7)

a) 3 2 C . C 4 11 P( X = 3) = —————————————— 5 C 15 P( X = 3 ) = 0,0733 ou 7,33%

b) P( X > 3 ) = P( X = 3) + P( X = 4 )