slides_psp1209_proba_2pp_petit - OER

1
!"#!"$% &'$
(')*'+,-./01 2'3456"67)8 6&7&$9#:'371 .1 ;21 ;< = /'>>'?'>@ A B0 /@ C/ 2=0'=@/',='D/=E'-.0;.FG/2'''' '''''''' '''''''' '''''''' '''''''' ''''''''
!"#$%&"'(
)('*&+(##(, -./&('#0
12)34,52)3,(#,2672
875.$/&"*
H.C=G1B'D/'I2JCK,G,L;/
!"#"$%"$&'()**
*+,-.(+/()01'.)'+()(")2('3)4#.$#56(%
7.15#5$6$"-%
7=II,01' M'GN/EI,2B',0.G'
!"#!"$% &'9
(')*'+,-./01 2'3456"67)8 6&7&$9#:'371 .1 ;21 ;< = /'>>'?'>@ A B0 /@ C/ 2=0'=@/',='D/=E'-.0;.FG/2'''' '''''''' '''''''' '''''''' '''''''' ''''''''
86-9(+"%)2()7.15#5$6$"-%
&$'?'>@10,D=C1;,@
&9'?'5.GC=G'D/'I0,F.F;G;1B2'2=0'D/2'B-B@/O/@12
&P'?'Q.0;.FG/2'.GB.1,;0/2'?'LB@B0.G;1B2'/1'G,;2'CG.22;<=/2
&R'?'SKB,0TO/'C/@10.G'G;O;1/'/1'C,OF;@.;2,@2'D/'-.0;.FG/2'.GB.1,;0/2

2
!"#!"$% &'P
(')*'+,-./01 2'3456"67)8 6&7&$9#:'371 .1 ;21 ;< = /'>>'?'>@ A B0 /@ C/ 2=0'=@/',='D/=E'-.0;.FG/2'''' '''''''' '''''''' '''''''' '''''''' ''''''''
86-9(+"%)2()7.15#5$6$"-%
&$'?'>@10,D=C1;,@
&9'?'5.GC=G'D/'I0,F.F;G;1B2'2=0'D/2'B-B@/O/@12
&P'?'Q.0;.FG/2'.GB.1,;0/2'?'LB@B0.G;1B2'/1'G,;2'CG.22;<=/2
&R'?'SKB,0TO/'C/@10.G'G;O;1/'/1'C,OF;@.;2,@2'D/'-.0;.FG/2'.GB.1,;0/2
!"#!"$% &'R
(')*'+,-./01 2'3456"67)8 6&7&$9#:'371 .1 ;21 ;< = /'>>'?'>@ A B0 /@ C/ 2=0'=@/',='D/=E'-.0;.FG/2'''' '''''''' '''''''' '''''''' '''''''' ''''''''

3
!"#!"$% &'U
(')*'+,-./01 2'3456"67)8 6&7&$9#:'371 .1 ;21 ;< = /'>>'?'>@ A B0 /@ C/ 2=0'=@/',='D/=E'-.0;.FG/2'''' '''''''' '''''''' '''''''' '''''''' ''''''''
86-9(+"%)2()7.15#5$6$"-%
7:);)*+".12'"$1+
5,@C/I12' @,=-/.=E'
VW,DTG/'I0,F.F;G;21/
VXCK.@1;GG,@'3I,I=G.1;,@
VY-B@/O/@1'ZQ.0;.FG/'.GB.1,;0/
!"#!"$% &'%
(')*'+,-./01 2'3456"67)8 6&7&$9#:'371 .1 ;21 ;< = /'>>'?'>@ A B0 /@ C/ 2=0'=@/',='D/=E'-.0;.FG/2'''' '''''''' '''''''' '''''''' '''''''' ''''''''
7:);)<=>-1.$(?)2(%)0.15#5$6$"-%);)@'1$)(")01'.)&'1$)A
[BA;@;1;,@'
V6.'\1KB,0;/' D/2' I0,F.F;G;1B2]' ,='\6/2'I0,F.F;G;1B2]' DB2;L@/@1'=@/'
F0.@CK/' D/2'O.1KBO.1;<=/2' <=;'A,=0@;1' =@'A,0O.G;2O/'/1'D/2',=1;G2' D/'
C.GC=G'I,=0' .@.GJ2/0',='10.;1/0' D/2'IKB@,OT@/2'.GB.1,;0/2*''
VYE/OIG/2'D/'IKB@,OT@/2' .GB.1,;0/2'?'G/'0B2=G1.1' D='^/1'DN=@'DB',='G/'
C,OI,01/O/@1' DN=@'C,@2,OO.1/=0*
W,1;-.1;,@'D.@2'=@'C,=02'D/'21.1'I,=0'G/2'I2JCK,G,L=/2
V6/2'I0,F.F;G;1B2' 2,@1';@D;2I/@2.FG/2' I,=0' A.;0/'D/'GN;@AB0/@C/' 21.1;21;<=/
VYGG/2'A,=0@;22/@1' G/2',=1;G2'I,=0' DBC0;0/' D/2'\ O,DTG/2'I0,F.F;G;21/2 ]'
I,=0' G/2'-.0;.FG/2',F2/0-B/2'2=0'G/2'I,I=G.1;,@' DN;@1B0_1' /1'G/2'O.@;I=G/0*
8II0,CK/'.D,I1B/'D.@2'C/'CK.I;10/
V&0B2/@1.1;,@' D/2'@,1;,@2' ;@D;2I/@2.FG/2' I,=0'G/'I2JCK,G,L=/'/1'I,=0'
A.;0/'D/'GN;@AB0/@C/' 21.1;21;<=/*
V41;G;2.1;,@' DN/E/OIG/2' 2;OIG;21/2'I,=0' L.0D/0'D='1/OI2'I,=0' G.'2=;1/*''
&G=2'DN/E/OIG/2' .=E'S&2*'

4
!"#!"$% &'`
(')*'+,-./01 2'3456"67)8 6&7&$9#:'371 .1 ;21 ;< = /'>>'?'>@ A B0 /@ C/ 2=0'=@/',='D/=E'-.0;.FG/2'''' '''''''' '''''''' '''''''' '''''''' ''''''''
7:);)7("$"()15%(.4#"$1+)2B'+)0>-+19C+()#6-#"1$.(
YEIB0;/@C/'?',@'^/11/'=@'DB'$9'A,;2
S.FG/.='D/'A0B<=/@C/2
aB2=G1.12
aB2=G1.12'D/2C0;I1;A2
X=
q0.5 = médiane = Etendue =
!"#!"$% &'!
(')*'+,-./01 2'3456"67)8 6&7&$9#:'371 .1 ;21 ;< = /'>>'?'>@ A B0 /@ C/ 2=0'=@/',='D/=E'-.0;.FG/2'''' '''''''' '''''''' '''''''' '''''''' ''''''''
7:);)@'(6&'(%)/1+/(0"%)2()5#%(
&KB@,OT@/',='/EIB0;/@C/'.GB.1,;0/
&KB@,OT@/',='/EIB0;/@C/' <=N,@' I/=1',0L.@;2/0' D,@1'G/'0B2=G1.1'@/'I/=1'
I.2'_10/'I0B-='M'GN.-.@C/*''YE?'^/1'D/'$'DB
Y-T@/O/@1
7,=2Z/@2/OFG/'D/'0B2=G1.12'I,22;FG/2' DN=@/'/EIB0;/@C/' .GB.1,;0/' 0BI,@D.@1'
M'=@/'C/01.;@/' C.0.C1B0;21;<=/*'
VYE?' 8'b' cF1/@;0'=@'@,OF0/'I.;0'b'd9e'Re'%f
Vg,1.1;,@'K.F;1=/GG/'?'G/110/'D='DBF=1'D/'GN.GIK.F/1
Q.0;.FG/'.GB.1,;0/
a/I0B2/@1.1;,@' @=OB0;<=/' D/2'0B2=G1.12' DN=@/' /EIB0;/@C/' .GB.1,;0/*''c@'
D;21;@L=/' G/2'-*.*'D;2C0T1/2'/1'C,@1;@=/2*
VYE?' h'b'0B2=G1.1'D='^/1' DN=@'DBe''i'b'j>',='I,;D2'DN=@';@D;-;D=
Vg,1.1;,@'K.F;1=/GG/'?'G/110/'O.^=2C=G/'D/'G.'A;@'D/'GN.GIK.F/1
&0,F.F;G;1B
g,OF0/' /@10/' #'/1' $e'<=;'D,@@/'G.' A0B<=/@C/' 1KB,0;<=/' ,='.11/@D=/'DN=@'
B-B@/O/@1*'c@'G.'DB1/0O;@/' 2,;1'2=0'F.2/'D/'A0B<=/@C/2' ,F2/0-B/2',='2=0'
F.2/'2=F^/C1;-/*'

5
!"#!"$% &':
(')*'+,-./01 2'3456"67)8 6&7&$9#:'371 .1 ;21 ;< = /'>>'?'>@ A B0 /@ C/ 2=0'=@/',='D/=E'-.0;.FG/2'''' '''''''' '''''''' '''''''' '''''''' ''''''''
7:);)D12C6()0.15#5$6$%"()01'.)6()E(")2B'+)2-)
h?'-.0;.FG/'.GB.1,;0/'0B2=G1.1'D='^/1'DN=@'DB
j=/G'1.FG/.='D/'A0B<=/@C/';DB.G'/1'O,J/@@/'2N.11/@DZ,@'M'.-,;0'I,=0'
C/11/'-.0;.FG/'k
S.FG/.=' D/'A0B<=/@C/' \ .11/@D= ]
c='[;210;F=1;,@' D/'I0,F.F;G;1B
W,J/@@/'.0;1KOB1;<=/' .11/@D=/
c='W,J/@@/'l',='Y2IB0.@C/'Ymhn
YE/OIG/'D/'C.GC=G' D/'I0,F.F;G;1B
&m8b,F1/@;0' =@'@,OF0/'I.;0n'b'
µ =
=E(X)=xiP(X=xi)
i=1
q
∑
!"#!"$% &'$#
(')*'+,-./01 2'3456"67)8 6&7&$9#:'371 .1 ;21 ;< = /'>>'?'>@ A B0 /@ C/ 2=0'=@/',='D/=E'-.0;.FG/2'''' '''''''' '''''''' '''''''' '''''''' ''''''''
7:);)D12C6()0.15#5$6$%"()(")*+,-.(+/(
W,DTG/'I0,F.F;G;21/
V4@/' D;210;F=1;,@' D/'I0,F.F;G;1B' /21'=@'O,DTG/'I0,F.F;G;21/' I,=0' DBC0;0/' G/'
C,OI,01/O/@1' DN=@/'2;OIG/'-.0;.FG/'.GB.1,;0/*''[/2'O,DTG/2'IG=2'
2,IK;21;<=B2' /E;21/@1' I,=0' DBC0;0/' \O.1KBO.1;<=/O/@1]' G/'
C,OI,01/O/@1' D/'IKB@,OT@/2' .GB.1,;0/2'IG=2'C,OIG/E/2*
V6/2'D,@@B/2' O.;2'.=22;'D/2'C,@@.;22.@C/2'2=F^/C1;-/2' 2,@1'=1;G;2B/2' I,=0'
C,@210=;0/' =@'O,DTG/'0BI,@D.@1' G/'O;/=E' I,22;FG/'M'G.'0B.G;1B*'
>@AB0/@C/
6N;@AB0/@C/' .'I,=0'F=1'D/'LB@B0.G;2/0'M'=@/'I,I=G.1;,@' D/2'0B2=G1.12'
,F2/0-B2'2=0'=@/'BCK.@1;GG,@' /E10.;1' D/'C/11/' I,I=G.1;,@*' '
>@AB0/@C/'/1'O,DTG/'I0,F.F;G;21/
V4@' O,DTG/'I0,F.F;G;21/' /21'=1;G;2B' I,=0' DBC0;0/' G/'IKB@,OT@/' DN;@1B0_1'
I,=0' G.'I,I=G.1;,@*' '>G'C,OI,01/' 2,=-/@1'D/2'I.0.OT10/2';@C,@@=2*
V 6N;@AB0/@C/' D,@@/'D/2',=1;G2' I,=0'/21;O/0' D/2'I.0.OT10/2' D='O,DTG/' M'
I.01;0' D/2'D,@@B/2' D/'GNBCK.@1;GG,@' /1",='B-.G=/0'G.'I/01;@/@C/'
DNKJI,1KT2/2' I0;2/2'D.@2'G/'O,DTG/*''8AA.;0/'M'2=;-0/'oooo