c c cc a
p p pp p ³SANTIAGO ANTÚNEZ DE MAYOLO´
p p p FACULT AD DE INGE NIERÍA DE MINAS GEOLOGÍ A Y MET ALÚRGIA
ESCUELA DE FORMACION PROFESIONAL DE INGE NIERÍA DE MINAS
ESTADISTICA APLICADA A LA INGENIERIA DE MINAS
PRESENTADA EN LA ASIGNATURA DE ESTADISTICA
p FLORES ISIDRO, Efraín
HUARAZ, 12 de Diciembre del 2011 p p p ~ ~ ~ p
p
pp
c c cc a
p p
V ! "V " # $ $ V $ % $ # $ ! $ % c p p
p
~ ~ ~ p
p
pp
c c cc a
p c pp p pcp p c c pcp p p p p p p p p p p p p p p p p
pp p p p pp pp p p ppp ! pp p p"p pp p # p p p p p ! p p p p p$ p % p p !p p &&p p p p
p ! p p p p p p p '&p p p
p p p p (p p p p p p p p p p p p p % p p p p p pp pp p p# p p p) p*& (p +pp p ,+p p p p p pp p pp p pp p p p p p p p p p -.p .//&p p p p p p p p p p p p p p p p p p p pp p p p p p p p p ,+p /0.11p p p p p p p p p p p p p p p p p p p p p p p p p p p p
p p p p
p p p p
p ppp p p p p' /p p p pp p p p Y! p ppp +p2,3pp $p4p.//&p5p -.p4p.166p 7p4p p8p..p p2'&3p4p// p4p6p
~ ~ ~ p
p
pp
c c cc a
ùp4p106p p 9: pp:;p 9 -.pp/-p?p 9/-pp 66?p 9 66pp /61?p 9 /61pp* 6 ?p 9* 6 pp*//-?p 9*//-pp. /'?p 9. /'pp.//*;p pp
#p 6p 0p p 'p &p 'p .p '&p
<p 6p */p .6p 1*p 1*p 16p '&p pp
"pp &.1p & -p &**p & p &p & p &&/p p
=p &.1p &'*p &61p &-1p &-1p &01p p pp
>p .1p -p **p &p &p &p /p &&@p
:p 1. 'p 0*-'p 1*''p 0**'p *1 0'p *0 /'p .1 .'p pp
p £p Y! p pp
+p
m
· '&· ' &·· '&&· · &'· &'· · · ·
p p p
p p> p2,3p !p p +p
p . / /pp
p £p Y! p pp
+p
à
$ & $ $p à $ $ $
p
p pp p p> p2,3p p p +p p4p
* -pp
£p Y p pp p
à
$p &
~ ~ ~ p
p
pp
c c cc a
p p% p p p p pp p p> p2,3p +p p4p &66/pp p £p Y! p pp
p A p
à
p
p
p A p p p +p p4p &*'.pp p £p Y! p p p pp p
$ $ p $ º $ $
2$ p p'&@p pp# p p p p,3p B*p4p
* -pp p
$ $ p $ $ $ $
2$ p p'&@p pp# p p p p,3p C'p4p
* -p p
~ ~ ~ p
p
pp
c c cc a
$ $ $p $ $ $ >/&p4p .'*1p
2$ p p/&@p pp# p p p p,3p p CC,DpD,CEDY,DpCpCD>$DFp £p ]p> p # +p
ù
( &
)
&
p
m p
ù
&
·&· p
p £p C p ! p # +p
ù
'& p p
£p Y # p p]+p
ù
p
p
U p
£p $ p +p
p p
p
Gp p
~ ~ ~ p
p
p p
c c cc a
& p
·& p $p4p * *p £p ]p +p
p
) ( &
&
m
p
p
&
'' p p
'& p p
*p Y! p pp pH +p2,3p $p4p/0.11p5p' /p4p/--*-p 7p4p p8p..p 2'&3p4p//p4p6p ùp4p0-.*/p 9: pp:;p 9' /p5p &.1-/p?p 9 &.1-/p*& - *p?p 9*& - *p5p.&& .-?p 9.&& .-p5p.0-1/1p?p 9.0-1/1p5p10/60p?p 910/60p5p'0' /p?p 9'0' /p5p/0.11*p;p D pp
#p *0p -p 0p *p &p p p '&p
<p *0p .6p 1/p 1-p 1-p 10p '&p pp
"pp &'-p & /p & -p &&1p &p &&*p &&*p p
=p &'-p &61p &0*p &0/p &0/p &0-p &&p pp
>p '-p /p -p 1p &p *p *p &&p
:p '1.*.p '*/10p *'&06'p .10.& p 116/*6p '1'0'.p /11*60p pp
p £p Y! p pp
+p
~ ~ ~ p
p
p p
c c cc a
m
·& &' ·&' &· '· ' ' & & ··'· &' ·
p p p
p pH p2,3p !p p +p
.---.p
p £p Y! p pp
+p
à
$ & $ $p à $ $ $
p
p pp p p p2,3p !p p +p p4p-00*.-p £p Y p pp p
à $p & p p% p p p p pp p pH p +p p4p/* -0 p p £p Y! p pp
p A p
à
p
p
p A p pp p pH p +p p4p &&&/ /p p £p Y! p p p pp p ~ ~ ~ p
p
pp
c c cc a
$ $ $p º $ $
2$ p 6'@p pp# p p p pH 3p B.p4p*&6*61'p p
$ $ $p $ $ $
2$ p -&@p pp# p p p p 3p C-p4p*.1'-6.p
$ $ $p $ $ $
2$ p p6&@p pp# p p p p 3p >6&p4p 66*.&'p p CC,DpD,CEDY,DpCpCD>$DFp £p ]p> p # +p
ù
&
)
( &
p p
Gp
m
ù
&
//I.*-p. *p
£p C p ! p # +p ù
*-0/-.p
~ ~ ~ p
p
p p
c c cc a
£p Y # p p]+p
ù
p
p
p
Gp
0*-/@p
£p $ p +p p p *&6*61'p
p
p
Gp p
Gp
p
16'1 0p
$p4p '06.*/p £p ]p +p
&
)
( &
m
p p
Gp
&
/06**-p
.&*6-p
~ ~ ~ p
p
p p
c c cc a
D,CDY,pJ],$,p p ,+p p p p p pp p pp p pp p p p p p p p p p p p p p p p p p p p p p p p p p p p p p pp p p p p p p p p ,+p p p p p p p p p p p p p p p p p p p p p p p p p p p p p
p p p p
p p p p
p ppp p p p pp p p pp p p £p Y! p pY # p pY p p p
+ Ë V )· ( pp Ë * '
p
+ '· & Ë V )· ( p Ë * '&
p
~ ~ ~ p
p
pp
c c cc a
p :2,3p pKp2,3
9' /5 &.1-/p 9 &.1-/ ?p *& - *?p
9*& - *5 .&& .-?p
9.&& .-5 .0-1/1p?p
9.0-1/1510/60p 910/605 ?p '0' /p?p
9'0' /5/0.11*p ;p
#p
9 -.pp/-p?p
d p
p
p
p
p
p
p
d p
9/-pp 66?p 9 66pp /61?p 9 /61pp * 6 ?p 9* 6 pp *//-?p 9*//-pp . /'?p
p
dp
dp
p
p
p
p
p
dp
p
p
p
p
p
p
ddp
p
p
dp
p
p
p
p
p
p
p
p
p
p
p
p
p
dp
p
dp
p
p
p
dp
p
9. /'pp.//*;p
dp
p
dp
p
p
dp
p
p
#p
p
p
p
p
p
dp
dp
p
~ ~ ~ p
p
pp
c c cc a
L4pp4p'&p p £p Y! p pp>
+p
p
m
p
p
p
m
. /p
p
p
p
.---.p
£p Y! p pp]+p
)
(
) (
) (
p p
m
)( -'*'-p
)
&
p
p
m
) (
p
(& p p
//I.*-p. *p
p öp dp p dp dp dp dp p dp dp p dp dp dp dp dp dp dp
p p p p p p p dp dp dp p p p p p dp p p
$p d p p dp p dp dp dp p p dp p dp dp dp p dp dp
p
ö$$p '· · &· · & '· · &'· ·· · ·'· · ·'· · & &· & &''· '·· · &· & & · ' ' ´ .&6 ''6* p
p#´
.&6Ip ''6* p
~ ~ ~ p
p
pp
c c cc a
p £p Y! p ppY +p p
) ()
) ! (
m
(
) ! ( 6-// *p p £p Y # p pY +p p
) ! (
&//p
) ( ) (
2 p p 3p p
p
p £p p pp$ +p p
p p
Gp
) ! ( ) (
p
Gp
p
p p
0*.p
p
Gp
61 /p
p üp
'& p
2p pp 3p
~ ~ ~ p
p
pp
d p p
~ ~ ~ p
p
pp
p
~ ~ ~ p
p
c
d d
d d c d
d
d
dp
p p
dp p
dp c p p p p p p p p p p p p p !p p p p p p p "p p p p p pp "p p p p p p p p p p p p "p p p p p pp p #p!p"p pp! p "p p " p p p p p p $p "p p p p p "pp p! pp pp p%p p ppp pp pp p p p p # ,
%
#
)-( · '
).(
&
&·
&·
'
·
·
£p / # ! ~ ~ ~ p
p
p p
dp p
ppp
d d
p
d d d
d
d
% p
öp
p
öp
öp
p
·
'
&&·
&
'
&
&
·
&·
&·
&·
'
&·
'
&&·
&·
·
·
&&·
·
·
&&·
&·
0
&
·
'·
&·
-. ~ ~ ~ p
p
pp
dp p
&
&
&
& )&() ( · )&()&(
´ '·
´ 1 '·)&(
´ '·
.´ 2 .´ '·2 '·- + -´ !.´ # -´ .´ '·2 '·) ( .´&3 # ~ ~ ~ p
p
p p
p p
£p p p p p p #
pp p
pp p
d d
d p
d d
d
d
p p
,
pp p
pp p
&
&
'· ) '() ( ) '() &( &
&&
£p cp p p ~ ~ ~ p
p
p p
dp p
'·U % /) ( ) ( 4& ´ 4& ´ ´& ) ( &
öppöp
&öp'pö p
p
p
dp
dp
d p
p
p
p
p
p
p
p
p
p
dp
dp
p
p
-´ &
m
) ( ) (&
~ ~ ~ p
p
pp
p p
m
) &( & &&
&
5 ´.6 57 5 ´ &)& ( 5 ) (´1·´ 5 ) (´2·´' # ' 57 £p p p p
&
ð
&
&
) (
)&( )() (
)· &
( )( & )'· ( ) ( &
&
'
~ ~ ~ p
p
pp