Cheat Sheef
absolute frequency relative frequency frequency function distribution function
now offen hi in normal
histogram step
by all hi
a hi step
occurs sum of
the Xi -
ni ->
H;.
↑is 1. everywhere least
at continous to the right histgram
amount
2. monotonically
increasing =-
limit 0 & width - Axis
3. lower upper limit
mediEaneven
Mode Arithmetic mean Geometric mean Harmonic mean
Highest sum R
frequency I amount=
6,- in
Quantile / Quartile
rit-quantile given-point y-Axis
-
follow until ifh its the =
point
al at that straightdown
on
graph
to y-Axis is result
YearlXnia*Xnqf b) if interval take &
->
or ithits mean
down to X-Axis
Measures of variation
mean absolute deviation
interquartie range quartile deviation
a as an das-az/+laz-an,
MAD à 414; -
-
=
2
=
①D= 2
variance standard deviation coefficientofvariation
54 E(Xi nj
=
-
1x +,
=
cu =
two dimensional distribution
Scaterprot Marginal distribution Conditional distribution
In z
hij *his hoj
De he Si Ehj./X- 4;sy=Ehijly: r
=
for i=1....k&j 1....independent=
-2 me
↳. nor 1 T =
Shi.Xii 4 hos li =
Variance of
sum
syy sy sy
=
+ +
2.2(yj -
y)14 4)
-
Covariance
difference -sit si-2. Ery-)/y- y
(y 2514j )(yi
= - -
4)
Correlation coefficient
independant Cyy 0
* =
hot other way around CA
(11 0 ->
y are dependent 54 Sy. Sy
=
SSE
rank correlation coeffient coefficient ofdetermination Yi a
=
bj
+
~5 TrgrX),rgry
=
R I",rie
=
Strabl- Ely:- Yi
↳
, Classical probability
↑A oteement
=
->
probability complementary A PA 1 -P(A) =
Conditional probability
->
impossible prob. Zero Dra) 0
has
event - =
Pra
->
events pairwise disjoint PrAnUAnU... An)-EPrAj pralB PrB =
->
difference SetAlB prAB) Pra) -PrAn =
=
->
2 arbitrary events->Prau)=PrA)+ prB)
-
Pran Stochastic independance
-> if A implies =1 = -> PrAl PrB
->
prob. two events simultaneously PrArb)=pra).pisia prai)=PrA &pIBIA pr) =
->
if independent prob. Thats simultan.-PrA1= prat.pr)
partion of it each event Al - > PrAr SprAlj).prj) pri).pri)
-> =
->
Bayes theorem In partition 2; P/B)
-
0 -> each ti holds Pli)=[pril. pri
4fal prob./partition Bayes theorem
He. n. ....
n fills sample +itj 0
=
space entirely HeuteU... Weil pril -
prior prob.; Plib)-> posteriori prob.
Distribution function Discrete random variables
1. each continuous to right a**(x+1y) *(y) 1. f(x) 0
=
=
at
2. monotonically
increasing Fal*(b), if acb 2. EfrXi) 1
=
3. lower limit o &
upper limit 1 3. From 1. & 2. if directly follows frei - 1
Density function xpected values
=
1. f(x) 0
frar a
=
=
Frx) 2...Sofrydx 1
=
=
(x) Exjf)4j)
= ->
if discrete
Variance random variables y=
= fre/axif continuously
V(x (1x =
-
xx)) Rules:
1. Constant al a
Standard deviation 2. Factor =(b.g(y) b. = 5g(y)]
=
3. Sum
(g1(x) g2(x)] ygn(x)] f(gz(X))
* =
+ +
Öx
=
+
Vy) 4. Linear transformation lath. 41 -ab. (y
Variances Standardization
1. Constant Val 0
=
-e
1
always mean O
2. Shift vixtal vix E 0 variance 1
=
=
3. Factor Vib.y bvrx)
=
Ob=(b10x
4. Linear transformation Vatb.y b. VIy =
Garb. (b/Ox
=
absolute frequency relative frequency frequency function distribution function
now offen hi in normal
histogram step
by all hi
a hi step
occurs sum of
the Xi -
ni ->
H;.
↑is 1. everywhere least
at continous to the right histgram
amount
2. monotonically
increasing =-
limit 0 & width - Axis
3. lower upper limit
mediEaneven
Mode Arithmetic mean Geometric mean Harmonic mean
Highest sum R
frequency I amount=
6,- in
Quantile / Quartile
rit-quantile given-point y-Axis
-
follow until ifh its the =
point
al at that straightdown
on
graph
to y-Axis is result
YearlXnia*Xnqf b) if interval take &
->
or ithits mean
down to X-Axis
Measures of variation
mean absolute deviation
interquartie range quartile deviation
a as an das-az/+laz-an,
MAD à 414; -
-
=
2
=
①D= 2
variance standard deviation coefficientofvariation
54 E(Xi nj
=
-
1x +,
=
cu =
two dimensional distribution
Scaterprot Marginal distribution Conditional distribution
In z
hij *his hoj
De he Si Ehj./X- 4;sy=Ehijly: r
=
for i=1....k&j 1....independent=
-2 me
↳. nor 1 T =
Shi.Xii 4 hos li =
Variance of
sum
syy sy sy
=
+ +
2.2(yj -
y)14 4)
-
Covariance
difference -sit si-2. Ery-)/y- y
(y 2514j )(yi
= - -
4)
Correlation coefficient
independant Cyy 0
* =
hot other way around CA
(11 0 ->
y are dependent 54 Sy. Sy
=
SSE
rank correlation coeffient coefficient ofdetermination Yi a
=
bj
+
~5 TrgrX),rgry
=
R I",rie
=
Strabl- Ely:- Yi
↳
, Classical probability
↑A oteement
=
->
probability complementary A PA 1 -P(A) =
Conditional probability
->
impossible prob. Zero Dra) 0
has
event - =
Pra
->
events pairwise disjoint PrAnUAnU... An)-EPrAj pralB PrB =
->
difference SetAlB prAB) Pra) -PrAn =
=
->
2 arbitrary events->Prau)=PrA)+ prB)
-
Pran Stochastic independance
-> if A implies =1 = -> PrAl PrB
->
prob. two events simultaneously PrArb)=pra).pisia prai)=PrA &pIBIA pr) =
->
if independent prob. Thats simultan.-PrA1= prat.pr)
partion of it each event Al - > PrAr SprAlj).prj) pri).pri)
-> =
->
Bayes theorem In partition 2; P/B)
-
0 -> each ti holds Pli)=[pril. pri
4fal prob./partition Bayes theorem
He. n. ....
n fills sample +itj 0
=
space entirely HeuteU... Weil pril -
prior prob.; Plib)-> posteriori prob.
Distribution function Discrete random variables
1. each continuous to right a**(x+1y) *(y) 1. f(x) 0
=
=
at
2. monotonically
increasing Fal*(b), if acb 2. EfrXi) 1
=
3. lower limit o &
upper limit 1 3. From 1. & 2. if directly follows frei - 1
Density function xpected values
=
1. f(x) 0
frar a
=
=
Frx) 2...Sofrydx 1
=
=
(x) Exjf)4j)
= ->
if discrete
Variance random variables y=
= fre/axif continuously
V(x (1x =
-
xx)) Rules:
1. Constant al a
Standard deviation 2. Factor =(b.g(y) b. = 5g(y)]
=
3. Sum
(g1(x) g2(x)] ygn(x)] f(gz(X))
* =
+ +
Öx
=
+
Vy) 4. Linear transformation lath. 41 -ab. (y
Variances Standardization
1. Constant Val 0
=
-e
1
always mean O
2. Shift vixtal vix E 0 variance 1
=
=
3. Factor Vib.y bvrx)
=
Ob=(b10x
4. Linear transformation Vatb.y b. VIy =
Garb. (b/Ox
=
