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Lotte's Probability Cheat Sheet (DRAFT) by

This is a draft cheat sheet. It is a work in progress and is not finished yet.

Discrete Distri­butions

Name
pmf
cdf
E(V);Var
Bernou­lli(p)
P(1)=p; P(0)=1-p
F(1)=1, F(0)=1-p
p;p(1-p)
Binomi­al(n,p)
P(k)=(­Nch­ooseK) pk (1-p)(n-k)
-
np;np(1-p)
Geomet­ric(p)
P(k)=(1-p)k-1 p
1 - (1-p)k
(1-p)/p; (1-p)/p2
Poisson(λ)
P(k)=e-λ λk/k!
-
λ;λ

Continuous Distri­butions

Name
pdf
cdf
EV;Var
Unifor­m[a,b]
f(x)= 1/(b-a) on [a,b]
F(x)=(­x-a­)/(b-a) on [a,b]
(b-a)/2; (b-a)2/12
Normal(μ,σ2)
-
-
μ;σ2
Expone­nti­al(λ)
f(x)=λe-λx
1 - e-λx
1/λ;1/λ2

Set theory

De Morgan's laws
(A∪B)c=Ac∩Bc &&&­& (A∩B)c=Ac∪Bc
Distri­butive laws:
(A∪B)∩C = (A∩C)∪­(B∩C) &&&­& (A∩B)∪C = (A∪C)∩­(B∪C)

Probab­ility

P(A∪B) = P(A) +P(B)−­P(A∩B)

NchooseK = n!/(k)­!(n-k)!

De totale kans is altijd 1! I.h.b. P(A)+P(Ac)=1

Condit­ional Probab­ility

P(A|B) =P(A∩B­)/P(B)
A&B indepe­ndent ⇒ P(A∩B) = P(A)P(B) & P(A|B)­=P(A)
Bayes' Theorem: P(A|B) = P(B|A)­P(A­)/P(B)

Er zijn n kleuren, ik kies er k. Ik heb ... opties

-
Volgorde maakt uit
Volgorde maakt niet uit
Kleuren mogen dubbel
nk
(n-1+k­)!/­(n-­1)!k!
Kleuren mogen niet dubbel
n!/(n-k)!
n!/k!(­n-k)!