Hallo,
ich soll prüfen, ob folgende Funktion eine Verteilungsfunktion ist.
Somit ist zu prüfen, ob die Funktion:
(i) zwischen 0 und 1 im Grenzfall verläuft
(ii) rechtsstetig ist (Prüfung der Sprungstelle bei 0)
(ii) monoton steigend ist.
Für e gilt: 0 < e < 1.
![](data:image/png;base64,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)
@ (i) Prüfung der Grenzwerte für +/- ∞
- ∞ : lim 1-e / (1 + e-y) = lim (1-e) / lim (1 + e-y) = 1- e / (1+e∞) = 0
∞ : lim e + 1-e / (1 + e-y) = lim (e) + lim (1-e) / lim (1 + e-y) = e + (1 - e) / (1 + e-∞ ) = e + (1 - e) / (1 + 0) = e + (1 - e) = 1
Daher wäre aus meiner Sicht dieser Punkt erfüllt.
@ (ii) Prüfung der Rechtsstetigkeit am Punkt 0:
lim gegen 0+: lim e + 1-e / (1 + e-y) = lim (e) + lim (1-e) / lim (1 + e-y) = e + (1 - e) / (1 + e-0) = e + (1 - e) / (1 + 1) = e + (1 - e) / 2 = Fy(0)
@ (iii) Prüfung monoton steigend
= Prüfung, ob Fy'(y) > 0:
für y<0: [1-e / (1 + e-y)]' = [(1-e) * (1 + e-y)-1]' =[Kettenregel] = (1-e) * (-1)*(1 + e-y)-2 *(- e-y) = (1-e) * (1 + e-y)-2 *(e-y) = ((1-e)*(e-y)) / (1 + e-y)2
für y>=0: Da sich die Funktion lediglich um eine Konstante unterscheidet, die bei der Ableitung ohnehin wegfällt, ist die 1. Ableitung gleich.
Kommentar Ergebnis > 0:
*) Zähler:
- (1-e) > 0 aufgrund Grenzen von e
- e-y > 0, da e-Funktion im negativen Bereich positiv ist / gegen 0 strebt.
*) Nenner: Quadrat von positivem Wert (siehe Argumentation von Zähler) bleibt positiv.
Daher ist die erste Ableitung > 0 und die Funktion monoton steigend.
Stimmt das alles so?
Vielen Dank für eure Hilfe!