Kurs : Mathematische Modellbildung/Themen/Schwangerschaft/W-Raum
Zugrundeliegender W-Raum
Bearbeiten
Ein W-Maß
P
{\displaystyle P}
Ω
=
{
0
,
1
}
{\displaystyle \Omega =\{0,1\}}
Bernoulli-Experiment →
P
{\displaystyle P}
p
T
r
e
f
f
e
r
:=
P
(
1
)
∈
[
0
,
1
]
{\displaystyle p_{Treffer}:=P({1})\in [0,1]}
Binomialverteilung: n-fache Wdh. des Bernoulli-Experiment , also Ergebnismenge:
Ω
=
{
0
,
1
}
n
{\displaystyle \Omega =\{0,1\}^{n}}
p
(
ω
1
,
.
.
.
,
ω
n
)
=
p
k
⋅
(
1
−
p
)
n
−
k
{\displaystyle p_{(\omega _{1},...,\omega _{n})}=p^{k}\cdot (1-p)^{n-k}}
k
=
ω
1
+
ω
2
+
.
.
.
+
ω
n
{\displaystyle k=\omega _{1}+\omega _{2}+...+\omega _{n}}
Binomialverteilte ZV:
X
:
{
0
,
1
}
n
→
{
0
,
1
,
.
.
.
,
n
}
{\displaystyle X:\{0,1\}^{n}\to \{0,1,...,n\}}
X
(
ω
)
:=
∑
i
=
1
n
ω
i
{\displaystyle X(\omega ):=\sum _{i=1}^{n}\omega _{i}}
ω
=
(
ω
1
,
ω
2
,
.
.
.
,
ω
n
)
∈
{
0
,
1
}
n
{\displaystyle \omega =(\omega _{1},\omega _{2},...,\omega _{n})\in \{0,1\}^{n}}
![{\displaystyle p_{Treffer}:=P({1})\in [0,1]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/49c41bed8ddab2e31da547322aa304011b931499)
