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Samenvatting begrippen hoofdstuk 2: toevalsveranderlijken
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hs 2:toevalsveranderlijken beschrijvende statistiek en kansrekenen alle termen en formules duidelijk op een rij
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discreet continukansmassafunctie fX(x) = pX(x) = P(X = x) (wordt niet gedef.)
1) 0 ≤ pX(x) ≤ 1 omdat P(X = x) = 0
2) ∑ pX(x) = 1
cummulatieve verdelingsfunctie FX (x) = P(X ≤ x) FX (x) = P(X ≤ x)
1) 0 ≤ FX(x) ≤ 1 1) het is een niet-dalende, positieve functie
met waarden kleiner dan 1.
2) limx→−∞ FX(x) = 0.
3) limx→∞ FX(x) = 1.
4) P(a ≤ X ≤ b) = FX(b) − FX(a)
kansdichtheidsfunctie (wordt niet gedef.) fX(x) = F'X(x)
1)Kansdichtheid is geen kans,
en dus niet beperkt tot waarden onder 1
2) FX(x) = −∞ ʃ x fX(u)du
3)P(a ≤ X ≤ b) = FX(b) − FX(a) = b ʃ a fX(x)dx
4) 0 ≤ fX (x), want het is de afgl vd niet- dalende
functie
kwantielfunctie QX(α) = xα ⇔ FX(xα) = α
de inverse van de cum. v. f.
Ze geeft voor elk getal tussen 0 en 1 weer
hoe groot de waarde is van xα zodat X
met kans α onder die waarde ligt.
mediaan: med(X) = QX(0, 5)
benedenkwartiel: QX(1/4)
bovenkwartiel: QX(3/4)
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