Teoria ryzykawywij, Studia, Różne, Notatki od Kamila, teoria estymacji punktowej + teoria ryzyka

[ Pobierz całość w formacie PDF ]
>PLJOCIeLK`PL`IPVXLTTV
d
`SP]_JOYZHUg]cYXVKV]PYRH"8`IPVXLTTV
d
`SP]_JOKVWVKQeLJPH
KLJ_`QP"`H
c
YB`IPVXLTXL`[SZHZg]"RZgXL`HSL
d
`eH`HXg]UVVKYZHU[
c
YXVKV]PYRHQHRPWVKQeLZLQ
KLJ_`QP$>HZ[XHSU_TQLYZ`KLaUPV]HUPLM[URJQP; , C!8*B]`VXLTZ-;"[2M#$
@X`LYZX`LcUWXVIHIPSPYZ_J`UeH"C252A
8
#UH`_]HT_TVKLSLTUPLWL]UVcYJP$4SH[YZHSVULNV
M08VK]`VXV]HUPL;K`PeLRPA
8
PUK[R[QLWL]PLUXV`RhHKWXH]KVWVKVIPLcUYZ]HTV
d
`SP]_JO
KV[`_YRHUPHXL`[SZHZg]$
Przykad
FHhg
d
`T_"
d
`L8-:@2<;"C-:D27;"A"7#-%2+"A"D#-%2("B-
A
B
=
92
;2625
NK`PL
=
9-;"72@#"
;-;"72<#"
6-;"D2<#"5-;"D2%#$Eg]J`
HYKSHKLJ_`QPM-!@!
=
=
; 6 5
%%2+%2(%
$
@V]YZHQL`HZLTW_ZHUPLRZgX_`XV`RhHKg]]_IXH
c
J"Z`U$ QHReHWVKQeH
c
JKLJ_`QeL$ :LKUeH
`TLZVK]_`UHJ`HUPHVWZ_THSULNVXV`RhHK[WVSLNHUHTHRY_T
HSP`HJQPVJ`LRP]HUL
Q
[
d
`_ZLJ`UVcYJP$FHhg
d
`T_"
d
`L[
d
`_ZLJ`UVcYcJKLJ_KLUZHKHUHQLYZWX`L`ZHILSeL
Z 5 6
THT_
Z 9
%2+%%%2(
"`HcYKSHKLJ_`QPM-!<!VZX`_T[QLT_
Z 9
; 6 5
=
; 9
] %'*&%
$
4SHM-!@!VJ`LRP]HUH[
d
`_ZLJ`UVcYcJ]_UVYP&% %2+$% %2(-+"`HcYKSHM-!<!VJ`LRP]HUH
[
d
`_ZLJ`UV
c
Y
c
JXg]UHQLYZ* %2+$' %2(-)2&$ET_
c
YSZLQ`HYHK_KLJ_KLUZWV]PUPLUWVKQeH
c
J
KLJ_`QeL!@!$
>PLJO"B26#IeLK`PLWX`LYZX`LUPeHTPLX`HSUeHWVK`IPVXg]]Y`_YZRPJOTV
d
`SP]_JOXL`[SZHZg]$
4SH[YZHSVULQKLJ_`QPMKLaUP[QLT_VK]`VXV]HUPL;
A
,C*B]`VXLT;
A
"[#-;"[2M#$
FHRhHKHT_"
d
`L;
A
QLYZVK]`VXV]HUPLTTPLX`HSU_T]`NSeLKLTWHX_*#JPHh5" 6$EZLK_
VK]`VXV]HUPL;
A
KLaUP[QLLSLTLUZSVYV]_"RZgXLNVXV`RhHKWXH]KVWVKVIPLcUYZ]HVRXLcYSVU_QLYZ
]`VXLTA
A
"7#-A
8
$
"706$2eLK`PLT_`HRhHKHcJKHSLQ"
d
`LKHUHQLYZWL]UHXVK`PUH
XV`RhHKg]A
/
-:A
A
,M08;UHWX`LYZX`LUPXL`[SZHZg]$E`]PeH`R[`Z_TUPLIeLK`PLWVZX`LI_
VRXLcYSHcJXLSHJQPWXLMLXLUJQPUH`IPVX`LXL`[SZHZg]"HSLXLSHJQeLWXLMLXLUJQPUH`IPVX`LXV`RhHKg]
TV
d
`SP]_JOXL`[SZHZg]$
;
A
"7#
Denicja
ALSHJQeL&]`IPVX`LBUH`_]HT_XLSHJQeHWXLMLXLUJQP"QLcYSP
P!3
N
#
,N
$
(7
Z
$
&Z
%
8Z
%
&Z
$
PP!3
N
#
,N
$
,N
%
(7
."Z
$
&Z
%
7Z
%
&Z
&
#-.Z
$
&Z
&
/$
?`UHJ`T_WX`L`c`IPgX]Y`_YZRPJOTV
d
`SP]_JOXV`RhHKg]WXH]KVWVKVIPLcUYZ]HUHB$
A_`_RPLTUH`_]HT_RH
d
`K_XV`RhHKWXH]KVWVKVIPLcUYZ]HA0c S[IRH
d
`KeHK_YZX_I[HUZeL
XV`RhHK[WXH]KVWVKVIPLcUYZ]HA0c"S[IRH
d
`KeH`TPLUUeHSVYV]eHGVXV`RhHK`PLA0c!$
EY`J`LNgSUV
c
YJPX_`_RHTPYeH]Y`_YZRPLLSLTLUZ_`A
/
$
'
 FKLaUP[QT_XLSHJQeL']`VXLT3
N
#
,N
$
(7
Z
$
'Z
%
-."Z
$
&Z
%
7Z
%
&Z
$
#$ALSHJQH'QLYZ
XLSHJQeHXg]UV]H
d
`UV
c
YJP$9UU_TWX`_RhHKV]_TYWVYVILT`KLaUPV]HUPHXLSHJQPQLYZZ
$
)Z
%
-.
.Z
$
&Z
%
7'"Z
%
&Z
$
#/$EVNgSU_TWX`_WHKR[XLSHJQHWXLMLXLUJQP]WXV]HK`HUHQLYZ`H`]_J`HQ
`HWVTVJeHWL]ULNVM[URJQVUHh[KLaUPV]HULNVUH`IPVX`LX_`_R$=PHXeHX_`_RHUH`_]HT_
KV]VSU_M[URJQVUHh' , c*
"NK`PLcQLYZ`IPVXLTX_`_R$Eg]J`HYXLSHJQeLWXLMLXLUJQP
TVd`LT_`KLaUPV]HcJQHRV3
6
#
,6
$
(W
A
$
&
%
A
%
-.'"A
$
#$'"A
%
#$
Przykad
>PLJO:IeLK`PL`IPVXLTK_YZX_I[HUZUH
$Eg]J`HYWX`_RhHKV]_TPTPHXHTPX_`_RYeH0
P!#":#-
9
`M:"`#
9
"`#"`##
%
M:"`#
PPP!!":#-J#":#$K"":#"J2K0
P\!)":#-
PP!"":#-
9
E"`#M:"`#"NK`PLE QLYZWL]UeHM[URJQeH$Eg]J`HY) QLYZVJ`LRP]HUeH
[
d
`_ZLJ`UVcYJPeH$
9
'
.P"&:"`##&/M`$
9
#
'
\!&":#-
P"&:"`##M`"NK`PLP,.%2&/*.%2&/QLYZM[URJQeH
#
XVYUeHJeH"P"%#-%"P"&#-&$EY`J`LNgSUV
c
YJPNK_PQLYZPKLUZ_J`UV
c
YJPeH]g]J`HYVZX`_T[QLT_
WX`_WHKLR P!$
\P!0":#-:
$
"&#QLYZXVK`HQLTYRhHKRPF JB
$
Przykad
>PLJOG-"G
$
21112G
K
#"NK`PLG
F
V`UHJ`H`]XVZ_`PU]LYZ_JQPQLKUVYZRV]LQ]R#Z_PUYZX[TLUZ
aUHUYV]_$@XVISLT]_IVX[WVXZMLSHYWXV]HK`HYPeLKVZHRPLQHSVRHJQPQLKUVYZRPRHWPZHh["
HI_[`_YRHcJVWZ_THSU_]`NSeLKLTKHULQXLSHJQPWXLMLXLUJQP`]XVZ`PU]LYZ_JQPWVXZMLSH$:L
d
`LSP
G
F
"R-&21112VYeHSPUPV]L"ZVH-a
$
G
$
$111$a
K
G
K
QLYZ`_YRPLTWVXZMLSH"NK`PLa
F
QLYZWXVJLUZLT
[K`PHh[RHWPZHh[`HPU]LYZV]HULNV]R#Z_PUYZX[TLUZ$FIPVXLTTV
d
`SP]_JOXL`[SZHZg]QLYZ
C(
K
"8-
*
+
7
K
"a
$
21112a
K
#,a
F
%%2
a
F
-&
"`HcYB(
VXH`'":
<
#-O"a#$FHZLTWXVISLT
F'$
]_IVX[VWZ_THSULNVWVXZMLSHWVSLNHUHY`[RHUP[TPUPT[T IeHKc`THRYPT[T!M[URJQPO"a#$
Przykad
>PLJO(IeLK`PLTPHXeHX_`_RH$4VIPLXHT_(]ZHRPYWVYgI"I_KSHYZXHZ_GVK_YZX_I[HUJPL:
;
VISPJ`VUHYRhHKRH]_UVYPhHA-("G#$>PLJOcIeLK`PL`IPVXLTX_`_RUPL[QLTU_JO$Eg]J`HY
(,c*
"
6:/;$>HQWXVYZY`_TWX`_WHKRPLTQLYZ("G#-9G$
Ag
d
`UPJeL("G#9G%%UH`_]HT_hHKV]HUPLT[IL`WPLJ`LUPH$
(
>PLJOG" H" I%%IeLKeH]PLSRVcYJPHTPX_`_R$Eg]J`HYTPHXHX_`_RH(TV
d
`LTPLcJ
UHYZeLW[QeHJL]hHYUV
c
YJP0
'$("G#%9G
($3
>##
("J#-J#IXHRUPL[`HYHKUPVULNVhHKV]HUPH[IL`WPLJ`LUPH
)$3
>##
("G$J#-("G#$J#`NVKUVcYcJ
*$3
>##
("JG#-J("G##WXVWVXJQVUHSUVcYcJ
+$("G$H#$("G#$("H##Y[IHKK_Z_]UVcYcJ
,$("G$H#-("G#$("H##HKK_Z_]UVcYcJ `]_RSL
d
`eHKHUHKSHX_`_RUPL`HSL
d
`U_JO!
-$G$
OP
H-.("G#$("H#
.$3
>( #,$!
.("G#-("H#-.("JG$"&J#I#-("JH$"&J#I#/$
@VKYZH]V]LXVK`HQLYRhHKLRZV0
'$("G#-9G
($("G#-"&$J#9G"J%%#YRhHKRH]HXZVcYJPVJ`LRP]HULQ
)$("G#-9G$JF JZG"J%%
*$("G#-9G$J
=
F JZG"J%%
+$("G#-9G$J
:>N;
0;
"J%%"9G 4%
0
$
9N
>;
>
46
J 4%
,$(
>
"G#-
J-%
$
9G
Lemat(nierwno·s·cLapunowa)
>PLJOG%%P%3 ^ 3 _ 3/$EZLK_"9G
R
#
#
4
$"9G
S
#
#
5
"WX`_J`_TUPLXg]UV
c
Y
c
JQLYZVYZXH
NK_GTHXV`RhHKUPL`KLNLULXV]HU_$
Dowd
FHYZVY[QLT_UPLXg]UVcYcJ:LUYLUHKSHM[URJQPQ"`#-`
5
4
PH-G
R
$=HT_
9G
S
-9Q"H#%Q"9H#-"9G
R
#
#
4
"
WX`_J`_TXg]UVcYcJ]UPLXg]UVcYJP:LUYLUH`HJOVK`P]ZLK_PZ_SRV]ZLK_"NK_HTHXV`RhHK
QLKUVW[URZV]_"J`_SPNK_GTHXV`RhHKQLKUVW[URZV]_$
5
4
-."9G
S
#
#
5
%"9G
R
#
Twierdzenie
FHhg
d
`T_"
d
`LG%%IeLK`PLZHRPL"
d
`L9N
>
"
;
3/KSHWL]ULNVJ
#
4%$EZLK_
'$(
>
QLYZ
c
YJP
c
YSLXVYUeHJeHM[URJQeHJKSHJ0"%2J
#
/"VPSLGTHXV`RhHKUPL`KLNLULXV]HU_
($435
>$#
!
(
>
"G#-9G
)$:L
d
`LSP9N
>;
3/KSH]Y`_YZRPJOJ 4%"ZV435
>$'
(
>
"G#-Z
1
,-897:\0
,:
;
"\#3&;$
)
 Dowd
'$FUPLXg]UV
c
YJP<HW[UV]HKSH%3 ^ 3 _ 3 J
#
THT_
$
%
$
%
#
4
#
5
=
=
9
G
R
3
9
G
S
=
=
=
(
R
"G#-
$
R
469
G-N
;
$
($4SHJ0"%2J
#
/THT_46"&$`#-`$W"`#"NK`PL435
T$#
G
R
3
$
S
469
G
S
-(
S
"G#"NK`PL
L T!
T
-%$BZeHK
!
"
!
"
$
>
469N
>;
-
$
>
9
N
>;
&
$W
9
N
>;
&
-
,
-
!
"
!
"
N
>;
&$
W
9
&
>$#
!
*9G$
-
$
>
9
N
>;
&
9.N
>;
/&
E
DC
F
%>$#
!
#
)$4SHJ 4%THT_
G$Z
1
-.N
>;
$N
>N
$
-.9N
>;
$9N
>N
$
-.469N
>;
$469N
>N
$
-JZ
1
-.
-.(
>
"G#-
$
>
469N
>;
$Z
1
$
0
%G$"
" G 4 "
&
&
&
$G$BZeHK
4SH%3 " 3 Z
1
`KLaUP[QT_G
-
$FKLaUPJQPG
]_UPRH"
d
`LG
N
>;
$N
>;
-.9N
>;
$9N
>;
7A"G$"#$N
>"
A"G 4 "#%N
>"
"&:
;
""##-.
-.J"$46"&:
;
""##$469N
>;
-."$
$
>
46"&:
;
""##$
$
>
469N
>;
-(
>
"G#$
FHZLT435
>$'
(
>
"G#%"$FKV]VSUV
c
YJP" 3 Z
1
UPLXg]UV
c
Y
c
J`HJOVK`PKSHZ
1
"Z`U$435
>$'
(
>
"G#%Z
1$
9
'
.&:
;
"\#/
#
0
M\"
BRhHKReHWXVWVXJQVUHSUeHKVOH`HXK[UH`_]HT_YRhHKReLWVYZHJP("G#-
#
#
4
#
4
-&:
X%&$?`UHJ`T_:
;
"\#-&.&:
;
/
$Eg]J`HYQL
d
`LSP G'O
;
"ZV
#
!
"
-
J
(
P!
M
$
BRhHKReHF JBUH`_]HT_YRhHKReLWVYZHJP ("G#-F JB
*
"G#-:
;
"\#-
A
AP
U
46:
;
"\#
#
#
$
"&/#"NK`PL
:
$
"a#-362:\0
,:"\#%a;$
Lemat
:L
d
`LSP:,
*
QLYZK_YZX_I[HUZeH"ZV
'$:
$
QLYZUPLTHSLQeHJH
($:QLYZWXH]VYZXVUUPLJPeHNhH
)$:
$
"a#$`-.a$:"`#$
Twierdzenie
:L
d
`LSPG':VXH`IQLYZ`TPLUUeHSVYV]eHVXV`RhHK`PLQLKUVYZHQU_TUHWX`LK`PHSL.%2&/KSH
WL]ULQWX`LYZX`LUPWXVIHIPSPYZ_J`ULQ" 252A#"ZV:
$
"I#THXV`RhHKVK_YZX_I[HUJPL:$
Dowd
FMHRZ["
d
`L:
$
"a#$`-.a$:"`#THT_A":
$
"I#$`#-A"I$:"`##-:"`#$
*
 Uwaga
9
$
9G-9:
$
"I#-
:
$
"\#M\$
#
@X`_W[
c
Y
c
JT_"
d
`LKHULQ]HXZV
c
YJPWPLUPeL
d
`ULQ`PUK_]PK[HSUPLKSHRH
d
`KLNVKLJ_KLUZHWX`_WPYHUH
QLYZ[
d
`_ZLJ`UVcYcJ^"RZgXHQLYZM[URJQeHXVYUeHJeH$@VYZ[S[QLYPeLXg]UPL
d
`"
d
`L^ QLYZ]ReLYhH
[
d
`_ZLJ`UVcYcJKSHTHh_JOWX`_XVYZg]WXV]HK`PKV]PeLRY`_JOWX`_XVYZg]]HXZVcYJPWPLUPeL
d
`ULQ
VXH`KSHTHh_JO`VZX`_T[QLT_]PeLRY`_WX`_XVYZUP
d
`KSHK[
d
`_JO!$>PLJO`_YR`PU]LYZ_JQP
VWPYHU_IeLK`PLK]PLTH`TPLUU_TPSVYV]_TPG"HV]HXZV
c
YJPHJOX`LJ`_]PYZ_JO$4SHK]gJO
KLJ_`QPGPHTV
d
`LT_WVXg]UHcJ[
d
`_ZLJ`UVcYJP9.^"G#/$9.^"H#/$4LJ_`QHWXV]HK`eHJHKV
]PeLRY`LQ[
d
`_ZLJ`UVcYJPQLYZSLWY`H$;H
d
`KeHM[URJQeL^,"K
$
2K
%
#*
XVYUeHJeHP]RSeLYheHUH`_]HcJ
IeLK`PLT_M[URJQeH[
d
`_ZLJ`UVcYJP$:L
d
`LSPGPHYeHYZXHZHTP"ZV[
d
`_ZLJ`UVcYJPTHQeHWVYZHcJ^"G#"
^"H#$FHRhHKHQeHJ"
d
`LYeHZV]PLSRVcYJPSVYV]LTV
d
`LT_WVSPJ`_cJPJOcYXLKUPL9^"G#%9^"H#$
FKLaUP[QT_M[URJQLWVTVJUPJ`eH_"G#-^"G#IeLKeHJeHM[URJQeHXVYUeHJeHP]_W[RheH$;H
d
`KeH
XVYUeHJeHP]_W[RheHM[URJQeL_,"K
$
2K
%
#*
"NK`PL"K
$
2K
%
#(
UH`_]HT_M[URJQeHYZXHZ_$
Denicja
ALSHJQeL)]`IPVX`L,UH`_]HT_J`eLcYJPV]_TWVX`eHKRPLT"QL
d
`LSP
P!3
T()
`)`
PP!3
T,U()
`)a7a)`-.`-a
PPP!3
T,U,V()
`)a7a)b-.`)b$
EWXV]HK`VU_JOKHSLQXV`]H
d
`HUPHJOQHRV,WX`_QTV]H
c
JIeLK`PLT_`IPgXX_`_RUH
$
Denicja
>PLJOG"HIeLKeH`TPLUU_TPSVYV]_TPV]HXZVcYJPHJOX`LJ`_]PYZ_JO$
P!@V]PLT_"
d
`L`TPLUUHSVYV]HGQLYZYZVJOHYZ_J`UPLTUPLQY`HVKH WVWX`LK`HH]WVX`eHKR[
YZVJOHYZ_J`U_T!PUHWPY`LT_G$
OP
HQL
c
YSPUPLXg]UV
c
Y
c
J
""#9P"G#$9P"H#
`HJOVK`PKSH]Y`_YZRPJOXVYUeHJ_JOM[URJQPP,
*
"KSHRZgX_JO]HXZVcYJPVJ`LRP]HUL9P"G#"
9P"H#PYZUPLQeHPYeHYRVcUJ`VUL$
PP!>PLJO9G
"
3/VXH`9H
"
3/$@V]PLT_"
d
`L`TPLUUHSVYV]HGQLYZTUPLQY`HVK
H]WVX`eHKR[YZVW#SVYY GWVWX`LK`HH]WVX`eHKR[YZVW#SVYY!PUHWPY`LT_G$
OI
H QLcYSP
""#`HJOVK`PKSH]Y`_YZRPJOXVYUeHJ_JOP]_W[Rh_JOM[URJQPP,
*
"KSHRZgX_JO]_YZeLW[QeHJL
]""#]HXZVcYJPVJ`LRP]HULPYZUPLQeHPYeHYRVcUJ`VUL$
PPP!>PLJO9"G#
"
3/VXH`9"H#
"
3/$@V]PLT_"
d
`L`TPLUUHSVYV]HGWVWX`LK`HH
]WVX`eHKR[XVYUeHJ_T]RSeLYh_TPUHWPY`LT_G$
F@R
H QL
c
YSP""#`HJOVK`PKSH]Y`_YZRPJO
XVYUeHJ_JOP]RSeLYh_JOM[URJQPP ,
*
"KSHRZgX_JO]HXZVcYJPVJ`LRP]HUL]""#PYZUPLQeH
PYeHYRVcUJ`VUL$
+
[ Pobierz całość w formacie PDF ]

  • zanotowane.pl
  • doc.pisz.pl
  • pdf.pisz.pl
  • mariusz147.htw.pl
  •