probabilidad y estadistica

5.1 f(x) =1/10, x = 1, 2, . . . , 10.
Por lo tanto P(X < 4) = 3 f(x) = 3/10
Σ
x=1

5.2 n = 12 y p = 0.5. por lo tanto
P(X = 3) = P(X ≤ 3) - P(X ≤ 2) = 0.0730 - 0.0193 = 0.0537.
10
10
5.3 µ =Σ x/10 = 5.5, y σ2 = Σ = (x-5.5)2/10 = 8.25.
x=1

x=1

5.4 n = 5 y p = 3/4, tenemos
(a) P(X = 2) = (52) (3/4)2 (1/4)3 ) = .0879
3
(b) P(X ≤ 3) = Σ b(x; 5, ¾) = 1 – P(X= 4) – P(X=5) = 1 –(54)(3/4)4(1/4)1 X=0
5
5
( 4)(3/4) (1/4)0 = 0.3672
5.5 a b(x; 20, 0.3).
(a) P(X ≥ 10) = 1 - P(X ≤ 9) = 1 - 0.9520 = 0.0480.
(b) P(X ≤ 4) = 0.2375.
(c) P(X = 5) = 0.1789.
P = .030
5.6 n = 6 y p =1/2.
(a) P(2 ≤ X ≤ 5) = P(X ≤ 5) - P(X ≤ 1) = 0.9844 - 0.1094.
(b) P(X < 3) = P(X ≤ 2) = 0.3438.
5.7 p = 0.7.
(a) n = 10, P(X < 5) = P(X ≤ 4) = 0.0474.
(b) n = 20, P(X < 10) = P(X ≤ 9) = 0.0171.5.8 n = 8 y p = 0.6, tenemos
(a) P(X = 3) = b(3; 8, 0.6) = P(X ≤ 3) - P(X ≤ 2) = 0.1737 - 0.0498 = 0.1239
(b) P(X ≥ 5) = 1 - P(X ≤ 4) = 1 - 0.4059 = 0.5941.
5.9 n = 15 y p = 0.25, tenemos
(a) P(3≤ X ≤ 6) = P(X ≤ 6) - P(X ≤ 2) = 0.9434 - 0.2361 = 0.7073.
(b) P(X < 4) = P(X ≤ 3) = 0.4613.
(c) P(X > 5) = 1 - P(X ≤ 5) = 1 - 0.8516 = 0.1484.
5.10 n = 12 y p = 0.7, tenemos
(a) P(7 ≤ X ≤ 9) =P(X ≤ 9) - P(X ≤ 6) = 0.7472 - 0.1178 = 0.6294.
(b) P(X ≤ 5) = 0.0386.
(c) P(X ≥ 8) = 1 - P(X ≤ 7) = 1 - 0.2763 = 0.7237.
5.11 n = 7 y p = 0.9, tenemos
P(X = 5) = P(X ≤ 5) - P(X ≤ 4) = 0.1497 -0.0257 = 0.1240

5.12 n = 9 y p = 0.25, tenemos P(X < 4) = 0.8343.
5.13 n = 5 y p = 0.7, tenemos
P(X ≥ 3) = 1 - P(X ≤ 2) = 1 - 0.1631 = 0.8369.
5.14
(a) n = 4, P(X = 4) = 1 - 0.3439 = 0.6561.
(b)[(63)(0.9)3(0.1)3] (0.9) = .0131
(c) la probabilidad de que los toros ganen es de 0.9
5.15 p = 0.4 y n = 5.
(a) P(X = 0) = 0.0778.
(b) P(X < 2) = P(X ≤ 1) = 0.3370.
(c) P(X > 3) = 1 - P(X ≤ 3) =1 - 0.9130 = 0.0870.
5.16 la probabilidad de 2 o mas de 4 motores operen cuando p= 0.6 es
P(X ≥ 2) = 1 - P(X ≤ 1) = 0.8208,
Y la probabilidad de 1 o mas de 2 motores operen cuando p= 0.6 es
P(X...