! Formuleblad!Statistiek!voor!Premaster! !
!
Week$1:$Discrete$variables$(finite$countable$number$of$outcomes)!
!"#$" = & ∪ ( = &) *")$+ )( = , & + ),(() A B
0"1*23*41#$" = & ∩ ( = &)*")( = , & ⋅ , ( !! A B
7#38$#"1 = & ∩ ( = )∅)(&)*")()ℎ*;;*")"#*13)<*=**"34ℎ>??*@#8A3)!! A B
!
Conditional)Probability)
D E∩F
B>"3)$?)&)>@3)()C$$2A$=1 = , & ( = s
D(F)
VB:)Dobbelsteen!!!A(‘even’)!=!{2,4,6};!B!(‘hoog’)!=!{4,5,6}!!!!
Q
D GHGI)GI)JKKL D M,O T
!!P(even|hoog)!=! = = R
S = !!
D JKKL D M,P,O U
Q
!
Probability)density)function)(pdf))&)cumulative)distribution)function)(cdf))
+ V = ), W = V → + V ≥ )0)*") +) V = 1!
\ V = ), W ≤ V → \ −∞ = 0)*")\(∞) = 1!
!
Expectation,)variance)and)standard)deviation)
Expectation!value!(mean)!=!` W = V+ V = a!
Variance!=!b W = c T = V − a T +(V)!!!Shortcut!=! V T + V − aT !
Standard!deviation!=!= d7 W = c = c )T !
!
Lineair)transformation)
af = > + ;ag
e = > + ;W → ) cfT = ; T cgT !
cf = |;|cg
!
Bernoulli)distribution:)succes)or)failure)
W~(*2" ? ) x! 0! 1!
` W = ?)>"j)b W = ?(1 − ?)! + V ! 1 − ?! ?!
!
Binomial)distributions:)series)of)trails)(n))succes)(k))or)failure)(l − k))
" m
W~(#" ", ? → + A = , W = A = ? 1 − ? Inm ))+$2)A = 0,1, … , "!
A
` W = "?)))>"j)))b W = "? 1 − ? !!!!!!!!!!!!!!!! Rekenmachine:! Im = ")"p2)A!
!
Week$2:$Continuous$random$variables$(all$values$in$interval$are$outcomes)$
, W = V = 0 → ?j+)#3)q3*@*33)‼ )+ V 4>@@*j)@#A*@#ℎ$$j)(s>>234ℎ#8"@#8Aℎ*#j)!
)
Uniform)distribution:)equally)likely)outcomes,)interval)[u, v])
z
W~! x, y )))))))))))))))))+ V = {n| )
0)
y
` W =x+ )
2
y−x T
b e = !
12
! 1!
!
Week$1:$Discrete$variables$(finite$countable$number$of$outcomes)!
!"#$" = & ∪ ( = &) *")$+ )( = , & + ),(() A B
0"1*23*41#$" = & ∩ ( = &)*")( = , & ⋅ , ( !! A B
7#38$#"1 = & ∩ ( = )∅)(&)*")()ℎ*;;*")"#*13)<*=**"34ℎ>??*@#8A3)!! A B
!
Conditional)Probability)
D E∩F
B>"3)$?)&)>@3)()C$$2A$=1 = , & ( = s
D(F)
VB:)Dobbelsteen!!!A(‘even’)!=!{2,4,6};!B!(‘hoog’)!=!{4,5,6}!!!!
Q
D GHGI)GI)JKKL D M,O T
!!P(even|hoog)!=! = = R
S = !!
D JKKL D M,P,O U
Q
!
Probability)density)function)(pdf))&)cumulative)distribution)function)(cdf))
+ V = ), W = V → + V ≥ )0)*") +) V = 1!
\ V = ), W ≤ V → \ −∞ = 0)*")\(∞) = 1!
!
Expectation,)variance)and)standard)deviation)
Expectation!value!(mean)!=!` W = V+ V = a!
Variance!=!b W = c T = V − a T +(V)!!!Shortcut!=! V T + V − aT !
Standard!deviation!=!= d7 W = c = c )T !
!
Lineair)transformation)
af = > + ;ag
e = > + ;W → ) cfT = ; T cgT !
cf = |;|cg
!
Bernoulli)distribution:)succes)or)failure)
W~(*2" ? ) x! 0! 1!
` W = ?)>"j)b W = ?(1 − ?)! + V ! 1 − ?! ?!
!
Binomial)distributions:)series)of)trails)(n))succes)(k))or)failure)(l − k))
" m
W~(#" ", ? → + A = , W = A = ? 1 − ? Inm ))+$2)A = 0,1, … , "!
A
` W = "?)))>"j)))b W = "? 1 − ? !!!!!!!!!!!!!!!! Rekenmachine:! Im = ")"p2)A!
!
Week$2:$Continuous$random$variables$(all$values$in$interval$are$outcomes)$
, W = V = 0 → ?j+)#3)q3*@*33)‼ )+ V 4>@@*j)@#A*@#ℎ$$j)(s>>234ℎ#8"@#8Aℎ*#j)!
)
Uniform)distribution:)equally)likely)outcomes,)interval)[u, v])
z
W~! x, y )))))))))))))))))+ V = {n| )
0)
y
` W =x+ )
2
y−x T
b e = !
12
! 1!
