U NIVERSIDAD DE SANTIAGO DE CHILE FACULTAD DE CIENCIA DEPARTAMENTO MATEMÁTICA Y CIENCIA DE LA COMPUTACIÓN ÁREA DE ESTADÍSTICA
PEP 1 Probabilidades y Estadística Estadística 10009 (06/05/2010) (06/05/2010)
Nombre:............................................................. Nombre:................................... .............................................Prof.:............ ...................Prof.:................................No!: ....................No!:
". Se #! $om%rob! $om%rob!&o &o '(e )!* !)e!$+ !)e!$+o,e* o,e* !morf!* !morf!* +e,e, +e,e, (,! e-$e)e, e-$e)e,ee re*+*e,$+! re*+*e,$+! ! )! $orro*+,. E, Corro*+, S$+e,$e /*e%+embre 01123 *e +,form &e )! re*+*+4+&!& &e (,! !)e!$+, !morf! &e #+erro5 boro 6 *+)+$+o &e*%(7* &e )! $r+*!)+8!$+,. Se re$o$+ero, &(r!,e (, $+ero +em%o /935 e-%re*!&o e, m+,(o*5 (,! m(e*r! &e "11 e*%e$me,e* &e e*! !)e!$+, ! 211;C. L(e1 >1= =21 TOTAL
Y Potencial de pasivación (en m)
=>01? =>11 1 "> @ 1 "2
=>11? =@1 " "1 >@
=@1? =@B1 1 B " " >1
TOTAL " @1 02 0 "11
"." Dee Deerm rm+, +,ee e) 1 '(e e* &+*$o,fo &+*$o,forme rme 6 &e*e! &e*e! $!mb+!r*e &e $om%!J!. Lo* $)+e,e* $o,forme* ,o &e*e!, $!mb+!r*e &e $om%!J!. U+)+8!,&o %ro%+e&!&e* 6 eorem!* &e %rob!b+)+&!&e*5 re*(e)4!: 0." S+ &e )! re<+,5 re<+,5 *e e)+
!"#$% !" &E PE'#E P'"'$$,*E&
E!
*$
P'+E,$ E*
+&"
-E
.$*.+*$-"'$&
P$+#$
".".= r 15>B1@ 1 (0p) E-+*e (,! re)!$+, &+re$! e,re )!* 4!r+!b)e*5 e* &e$+r5 !) !(me,!r e) +em%o &e re $o$+m+e,o5 !(me,! e) %oe,$+!) &e %!*+4!$+,. (0p) 121 X = @AA5AADmV /1.0 p3
/ −
@AA5AAD = −>11 +
20 ⋅ k "
−
"11
"23 ⋅ 01 ⇒
@>
k "
=
>D.ACG /1.> p 3
C1G − >D5ACG = 15"CG/1.@ P 3
E) 15" &e )o* e*%e$me,e* +e,e, (, %oe,$+!) &e %!*+4!$+, e,re Me V ".0.0 Me
>11 +
= −
/@B − "23 ⋅ 01 @>
@AA5A0 /1.0 p 3
= −
L! &+*r+b($+, e* b!*!,e *+m7r+$!5 e) %rome&+o e* m(6 $er$!,o ! )! me&+!,! 6 e*!* &o* me&+&!* e*, ! *( 4e8 m(6 $er$! &e) $e,ro &e) re$orr+&o &e )! 4!r+!b)e /@1mV3 Co,fe$$+, &e) %o)% A$#(r!r e) re!: 1."% Co,$)(*+,: 1.0%
".@ CV /Y 3 =
X
=
>052
">5 >C> − @AC .> s X
=
= −
151@A
"C5BC
/1.0 P 3
/1.0 P 3
15 9 150 CV/Y3 CV/3 "> 5ABA /1.> p 3 = 15@BD >1 5@"C ∴ La distribución del potenci al de pasivación es más #om ogénea / 1 . 0 p 3 CV /W 3
0.
=
Se!, )o* *($e*o*: A L! %er*o,! +e,e $e)()!r &e )! $om%!J! A K L! %er*o,! +e,e $e)()!r &e )! $om%!J! K C L! %er*o,! +e,e $e)()!r &e )! $om%!J! C D L! %er*o,! e* &+*$o,forme $o, e) *er4+$+o V L! %er*o,! &e*e! $!mb+!r $om%!J! P/A3 15B P/K3 150 P/C3 15" P/DQA3 15 P/DQK3 15 P/DQC3 152 P/VQ DA3 152 P/ VCD3 151B@ P/DVQK3 15> /1.0% %or &ef+,+r *($e*o*3
0."." 1." % %or %o,er )! %re<(,! /1.> %or re*%(e*! $orre$!3 0.".0 P/V3 /1."%3 P /V 3 = P /V Q ∩ D3 ⋅ P / ∩ D 3 + P /V Q B ∩ D3 ⋅ P / B ∩ D3 + P /V Q C ∩ D 3 ⋅ P /C ∩ D 3 P /V 3 = P /V Q ∩ D3 ⋅ P / ∩ D 3 + P /V ∩ B ∩ D 3 + P /V ∩ C ∩ D 3 P /V 3 = 1521 ⋅ 15B1 ⋅ 15CC + 15>1 ⋅ 150C + 151B@ = 15@D>
/1.B p 3
0.".@ 1."% %or %o,er )! %re<(,! 5 1. %or re*()!&o 6 o&o $orre$o 0.0 Se! A+ L! %er*o,! + +e,e $e)()!r &e A? + "505@ P/A +3 15B E A )o me,o* &o* %er*o,!* +e,e, $e)()!r &e A P/E3 P /A"A0A@$3 U/A"A0 $ A@3U/A"$ A0A@3U/A"A0A@3 1.0% P/E3 @15B015> 15B@ 15B> /1.>%3
