Download Probability and Statistics Formulas and more Lecture notes Introduction to Econometrics in PDF only on Docsity! Variobla combinud
fe poote Qua Af Valoare din interval
le sp cosacteni2enB® prin p fumekia Cumulata de erdoabilitate — FO)
(Puwrtio. de cepartitic)
Rumekia densitate de probariatate (+)
F(X) = P(X <x)
ab moaxb > P(a=XK=b) = Tb) - F(a)
-1(X<b) - P(K<a)
Funcia demeitate de probalntutate
Reoprickesi :
A. Rin oO
2. Aa ee de “oe tou Prronekt ei, gontru toate
walortle Rex XK eat].
3. ab cuach > P(A<X<b) = 5 f(x) dx
by a
= J f09 dx- | Fx) dx
b Fle) PUKE X)= J £9 ax
Ko
Hedin: €(X) = Kh Variant t fx =€ tei-p)
Legi de probabilitake continue
L. Lecea normale
2. legen his-patrat (X)
%. legen Student
4h. Lecea Tider
Ss. lecea loge normana
G. Lega expenemparer
@ lenec Normale de Probarilctate
Le» importanfe : ~ poate aprouma distribxfig mubter ecnclle Aleatoare
~ diskributta, medied de egamticnare ese Mermala Conform Teoremet Lima
- Fl Comteater
~ Caloutul probaleitctaglor ake relaky Simply
- $-G Comatatat c& duce la dewey foune.
Le carackenittiad: - se baxenRn FR doar 2 pacamey | ph vT
— este Fimetried fata de medie
d) Estimator Consystesrt : TS S50 cand n>00
Goo
el6-S
ls diferema dintre, Valeared asteplaka a. €ehmatoruluy
& Poscmerts tinde catre 0 Gd Yelumul
Canionulur creche pre infinit>
A nw “w
3) Estimator eficient -O, Sa. - varie aor
2 a2 ~ a
&<%, (glow
Les bintre mai multi estimated nedeplacai, este elecent co? Cur
Variant mai mica. iw
OB, 7 ma Ricient
Hodotitdii de ice Q estimateriler « Exemple de eskmaten :
* T. Bor wai onic paitrake, > GR
VAL wercrsonilitadi wndoume RETR ae
WM opecaigota & momantder ‘ Proportio
eke. * volum
0 parame made ele,
N
Hedin de egantionare (Sample mean): YX
£e consider 0 Populate. AK de Vou N chservata ta mpork Oo % |
de medie X si abatere Ty § extragem efantionul de volum WL
(dor » extragen,, Ci Se oscoiagm vectorul Ky Xo... Ky
XX => paramerra(necancstut) Fimedra recta din populatie.
A
XX => mediq de esantonrare
Ke
Kythot Ka
“
e( %) <e( See) = [er )setsay reba) -Lnk
Ro
E(X) =y => Media de esantionare eke LW) estimator contrat
T (x)= q (Ae) ~Faldlx)+1st,)|
= (x)
\?
_%&
PS
vf
) X x CN () =K
A
\% q (X)- Sx — Gnd egantonses,
WW foce Cu Pevenire
s{k)- £ Cand esantionarea foce.
a fare revenire
Pace de coreche
BY o.1 > W diferente imtre tele 2 tipuri ce eyantionad
cient he
eas exaust vibake
A ~ (a
Y=>3-% EW) XK EN (6,1)
TY” G
“Teorema Limita contrale( Tc)
Suma a 1 Voriabite Imdepondene de aceergi lege de prebabittale (tcsreta/comtnua)
urmeza. leyec Normala de probabilitate camd > 00.
XX, eK yt. Xn
E(X)- E(K, tKote +X a)= E(Ki) +. + E(X Kn) = ak
Nietrbacia Varianter din esantion este laa ye (hipaa)
nea x7
Se considers extryert dinkr-o Pepwlatie distribute Normal , de medie K, vartanta don pepulate
IEF Variant dn eaten RY.
e
Expresia ' _ Urmecse: Camphetic) 0 lag x ww Vent Grade de libertate
z “
No |
(pe maura ce a crepte)
Legea a Pace legitur, dintre populatie si epantion
A
E(%j-X). Ne a
(WD OTT BWR) s(x) 5 a
es wT, TK Tx
L
lesen X = Suma a 0 variable normale independente Cortate 9 reduce (2) ridicate la peatrat-
KN > lerea KE eake. defi
poethy, este Rimebrica
3 Ore 0 (onda Alpe ter
le dreapta.
f 4) & £& deplaseaac la dheapta,
ny)
Tatervalil de rerio penn variant:
P(X 2 eK =k
DOE onc
x
q [odes Nay geal.
L
X taba.
Cay
&
| eae Student
le fepreaiontd lecea de probabiétate 0 medtes cand varante reale (din populate) nu x Cudeage
6% Tnlccuieste Cu vanante din egantion (4%)
Le ose Pawar In egantiogne mici (n< 80)
Loo variatla Student ete faportal dimbre @ vanabila Normala contrudd Fi redusd §i
i . 2
Wadena patrate a Lume leg % aiviaatt tu (per do kcbertate-
x
K-K x
Tx A = X-K
= = Student Cu d= M4
t= eo — -XK. & ata € gfraste de Labentete
x oe Aw wi
yD Te wm
n ,
Cotcluaie I Cath iy Care Nu Ae Cumreaste Yaniamta dim populate, media cin Esamtion Lurmenté o lege
Studemt tw 0 <0 qa ck Cibertate.
Amtervalut de ‘tmeredere al mmedied Chmd TZ mu se cumeane:
P(-timmsts Las.) = dk
