1.1.2: (a) 125 (b) 60 1.1.3: (a) 13983816 (b) 10000000 (c) 177147

1.1.2: (a) 125
(b) 60
1.1.3: (a) 13983816
(b) 10000000
(c) 177147
1.1.4: (a) 1
(b) 246820
(c) 2600624
1.1.5: 529000 bzw. 528471
1.1.6: n ≥ 4 bzw. n ≥ 5
1.3.1: P (A ∩ B) = 0,05, P (A ∩ B) = 0,5, P (A ∩ B) ∪ (A ∩ B) = 0,3
1.3.2: (a) P (B) = P (A ∩ B) + P (A ∩ B) ≥ P (A ∩ B) = P (A)
(b) P (C) ≥ P (A ∩ B) = P (A) + P (B) − P (A ∪ B) ≥ P (A) + P (B) − 1
1.3.3: 0,488
1.3.4:
1
6
1.3.5: (a) 0,5177
(b) 0,4914
· N −M
(M
m ) ( n−m )
(Nn )
(b) 0,3484
1.3.6: (a)
1.3.7: n ≥ 4
1.3.8: 0,9684
1.3.9:
1.3.10:
1
6
(a−2rs −2rk )·(b−2rs −2rk )
ab
1.4.1: 0,1
1.4.2:
p
8−7p
1.4.3: (a) 0,845
(b) 0,0968
1.4.4: (a) 0,0317
(b) 0,4940
1.4.5: (a) 0,35
(b) 0,6154
1.4.6: 0,75
1
1.4.7: 0,9947
1.5.1: Ja
1.5.2: (a) (1 − p) · p
(b) p
(c) p + (1 − p) · p
1.5.3: (a)
(b)
(c)
(d)
1
24
1
4
1
4
17
24
1.5.4: (a) 1 − (1 − q)m
(b) 0,001
1.5.5: (a) 0,168
(b) 0,24 und 0,3293
1.5.6: (a) 0,8928
(b) 0,93
(c) 0,9746
(d) 0,9165
1.5.7: (a) 0,1072
(b) 0,8064
1.5.8: (a) 0,1593
(b) 0,6431
1.5.9: 2 Druck- und 2 Temperatursensoren mit Wahrscheinlichkeit 0,9009
2.1.1: (a) c =
1
6
(b) P (X < 2) = 12 , P (X ≤ 2) = 1, P (0 < X < 2) =
(c) E(X) = 34 , Var(X) =
5
9
(d) x = 2
2.1.2: (a) c = 0,2


0
, falls x < 0,





0,5 , falls 0 ≤ x < 1,
(b) FX (x) = P (X ≤ x) = 0,7 , falls 1 ≤ x < 2,


0,8 , falls 2 ≤ x < 3,




1
, falls x ≥ 3,
E(X) = 1, Var(X) = 1,4, σ(X) = 1,183
2.1.3:
k
0
1
2
P (X = k) 0,009 0,208 0,707
E(X) = 1,85, Var(X) = 0,2975
3
0,076
2
1
3
2.1.4: (a)
k
0
1
2
3
P (X = k) 0,5 0,25 0,125 0,0625
E(X) = 0,96875, Var(X) = 1,655
4
0,03125
(b) 0,03125
2.1.5: (a) P (X = k) = (1 − p)k−1 · p (k = 1,2, . . .)
(b) 0,0961
(c) 0,9044
(d) E(X) =
1
p
2.1.6: (a) 0,2364
(b) 0,0980
2.1.7: (a) 0,0966
(b) 0,0365
2.1.8: 0,7443
2.1.9: 0,8322
2.1.10: (a) 0,2275
(b) 0,6472
2.1.11: 0,1808
2.1.12: (a) E(X) = 2,5
(b) 0,0980
(c) n = 25
2.1.13: n = 10
2.1.14: 0,4493
2.1.15: (a) 0,5034
(b) 0,0498
2.1.16: (a) 0,6321
(b) 0,0183
2.2.1: (a) c =
2
3


0
, falls x < 1,
(b) F (x) =
− 1) , falls 1 ≤ x < 2,

1
, falls x ≥ 2,
14
E(X) = 9 , Var(X) = 0,0802, σ(X) = 0,2833


0 , falls x < 0, √
2.2.2: (a) f (x) = x , falls 0 < x < 2,


0 , falls x > 2
1 2
(x
3
(b) E(X) = 0,9428, Var(X) = 0,1111
3
5
0,03125
2.2.3: (a) 0,3935
(b) 0,3834
(c) x = 2,773
2.2.4: E(X) = 1738,03, x = 1204,71
2.2.5: (a) 0,4031
(b) 0,3563
(c) 0,3842
2.2.6: (a) 0,6321
(b) 0,2650 und 0,3217
2.2.7: (a) 0,8664, 0,8228, 0,8413
(b) 0,8186, 0,1359, 0,6306
(c) σ 2 = 4
(d) µ = 8,798
2.2.8: 0,0441
2.2.9: (a) 0,9759
(b) 0,9876
(c) σ = 6,06
2.2.10: (a) 65
(b) µ = 150,36
2.2.11: (a) 0,0228
(b) 122,775
(c) µ = 75,165
2.2.12: (a) 0,095
(b) c = 0,0588
2.3.1: (a) E(Y1 ) = 320, Var(Y1 ) = 17, E(Y2 ) = 320, Var(Y2 ) = 25
(b) Y1 ∼ N (320,17), Y2 ∼ N (320,25)
(c) P (|Y1 − 320| < 12) = 0,9964, P (|Y2 − 320| < 12) = 0,9836
2.3.2: (a) Y1 ∼ N (0,4)
(b) Y2 ∼ N (µ,σ 2 )
2.3.3: F (x) = 1 − e−λx
2.3.4: 0,971
2.3.6: (a) 0,2112
(b) n ≥ 3
2.3.7: (a) 0,0023
4
(b) n ≤ 36
2.3.9: (a) 0,2277
(b) 0,9244
2.3.10: (a) 0,0968
(b) 0,2078
2.4.1: (a) 0,9207
(b) 0,9216
2.4.2: (a) 0,0287
(b) n ≥ 58
2.4.3: n ≥ 120
2.4.4: n ≥ 72
2.4.5: (a) 0,352
(b) 0,648
2.4.6: (a) p = 0,03
(b) 0,3528
2.4.7: (a) 0,0166
(b) 0,9608
2.4.8: (a) 0,9642
(b) n ≥ 167
(c) 0,75 und n ≥ 2500
5