VBLES. ALEATORIAS Y PRINCIPALES DISTRIBUCIONES
Estad´ıstica (10Grado de ADE) - 2015/2016
1. (a) E(X)=2.44, Mo = 3 y x0.6= 3
(b) E(1200X) = 2928 euros, σ1200X= 1716.6 euros
(c) P(X= 2.5) = 0, P(X > 0/X ≤4) = 0.8696 y P(X > 2) = 0.54
2. (a) xi0 1 2 3 4
pi0.35 0.25 0.2 0.1 0.1
(b) E(X) = 1.35, Me = 1, M o = 0, σ= 1.3143
(c) P(X > 2) = 0.2, P(1 ≤X < 4) = 0.55
3. (a) k=1
4
(b) Por simetr´ıa E(X) = Me = 2. Adem´as M o = 2
(c) F(x) =
0 si x < 0
x2
8si 0 ≤x < 2
x−x2
8−1 si 2 ≤x < 4
1 si x≥4
4. (a) k=2
25,E(X) = 3.5067
(b) P(X < 5/X > 3) = 0.75
(c) E(100 + 2X) = 107.01 euros.
5. (a)F(x) =
0 si x < 0
5x4−4x5si 0 ≤x < 1
1 si x≥1
(b) P(X > 0.4) = 0.91296
(c) E(X) = 2
3
6. (a) 0.1209
(b) 0.2019
(c) 0.9144
7. (a) 0.5
8. (a) 0.0591
(b) 0.2231
(c) 0.1733
9. (a) 0.0487
(b) 38 componentes.
(c) 1
