Laboratorio sesion 3

La p!ba p!bab"#" b"#"dad dad d$ d$ $&$ $&$ 'n p$na p$na#& #& a Ca"# Ca"##a #a $ $ d ,c$& c$&a a 4 p$n p$na# a#&" &"$ $ b) ,c$& c$&a a n"n n"n'n 'n! ! (a (a## ##a a &!

PROBLEMA 1

DATOS

p q n

D

80% = 1-p = 10

0.8 0.2

a) p(x=4) b) p(x=0) C) P(X=1d) p(3< p(3<=x =x<= <=6) 6) = p(x=3) p(x=4) p(x=5) p(x=6) p(3<=x<=6) =

a##a #a p!bab"#"dad d$ q'$ #ana 'n dad! cb"c! c'a&! c"nc!. c) n n$! d$

PROBLEMA 2

DATOS

p q n

1 /6 5 /6 20

a) p(x>=1) b) c) p(3<=x<=5) = p(x=3) p(x=4) p(x=5) p(3<=x<=5) =

n 'n d$&$"nad! d$&$"nad! '$! d$ d$ 'n ca"n! ca"n! $ $ ana c'and PROBLEMA 3 " $ $x&a$n a# aa 15 ca&a "$p$ c!n $$p#a !ca"! !ca"!n$. n$. b) b) La p!ba p!bab"#" b"#"dad dad d

DATOS

p= 40/4 = q= n=

PROBLEMA 4

0.1 0.9 15

D

a) p(x=4) b) p(x=0)

$ 'n 'na a 'na 'na q' q'$ $ c!n $n$ $n$ 'n 'na a ! a anc anc $$ $$p#a #aa"$n "$n&!. LL LLaa a! X a# n n$! $! d$ d$ b! b!#a #a b# b# d"&"b'c"n d"&"b'c"n d$ p!bab"# p!bab"#"dad "dad d$ X b):C';# b):C';# $ ' $d" b!#

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DATOS

p

1/ 3

q n

2/ 3 5

p(X=x) = µ=n.p σ= B(..) c) p(x>=2) = p(x=0) p(x=1)

n &a& &a&a"$ a"$n&! n&! c!n c!n&a &a $# c;nc$ c;nc$ p!d' p!d'c$ c$ 'na 'na $! $! '"n"& '" n"&a a a c"n c"nc! c! pac pac"$n& "$n&$ $ ca# ca#c'# c'#a+ a+ a) a) La p p!ba !bab"# b"#"d "d q'$ a# $n! $!$n &$ pac"$n&$.

PROBLEMA 5

p q n

a) b)

,?@ 0.8 0.2 5

a) p(x=5) b) (p(x<=3)= p(x=3) p(x=4) p(x=5) p(x<=3) = c) µ=n.p

*a 'n &!&a# d$ 50 &abaad!$ :C';# $ #a p!ba $

PROBLEMA 6

DATOS

p q n

DESA

0.08 0.92 50

p(x<=2) = P(X=0) P(X=1) P(X=2) RPTA =

PROBLEMA 7

La p!bab"#"dad d$ 'n a&"c'#! q'$ $a d$$c&'!! $n $p$ $p$c& c&" "a a p!b p!bab ab"# "#"d "dad ad$ $ d$ q'$ q'$ 01 012 23 34 4  5 a&" a&"c c



q n

PROBLEMA 8

0.94 5

P(X=1) P(X=2) P(X=3) P(X=4) P(X=5)

n 10 10% % d$ d$ #! #! $p# $p#$a $ad! d!  d$ d$ p p!d'c !d'cc c"n "n $n d$& d$&$" $" da $n $# a7!. 'pna$ q'$ $ $#$cc"!nan a# aa a'$n&"!. a) :C';# $ #a a"ab#$ a#$a&!"a b) :#a p!ba p!bab"#" b"#"&"c &"ca a b"n!"a# b"n!"a# paa paa $# $xp$" $xp$"$n& $n&! ! d) :c' $#$ $#$cc cc"! "!na nad! d!  $& $&  a' a'$n $n&$ &$  $) $) ca# ca#c' c'#a #a $ $

DATOS

p q n

10% 90% 10

0.1 0.9

a) x=  $p#$ad! b)  'na a"ab#$ c)

p(X=x) = D/

d) p(x=0) $) µ=n.p σ=B(..) E2 =  E2 a"na=



$# 80% " &"a! 10 p$na#&"$ *a##a #a p!bab"#"dad d$+ a) !) c) ,c$&a ,c$&a a#'n! d) ,c$&a $n&$ 3  6 p$na#&"$.

ESARROLLO

0.006 1.024-00F 1.024-00F p(x=3)Gp(x=4)Gp(x=5)Gp(x=6) 0.001 0.006 0.026 0.088 0.121 0 $c$ !b&$na!+ a) ,# $n! 'n c"nc!. b) xac&a$n&$ c"nc! c!p$nd"d! $n&$ &$  c"nc!.

DESARROLLO

= 1-p(x<1) = 1-p(x=0) p(x=4) p(x=3)Gp(x=4)Gp(x=5) 0.24 0.20 0.13 0.5F

0.9F 0.20

a# $x&a$ 'na ca&a d$ 'na baaa $pa7!#a !b&"$n$ 'n a. "$n&! $ p"d$+ a) La p!bab"#"dad d$ q'$ an$ $xac&a$n&$ q'$ p"$da #a 15 $c$ q'$ $ '$a.

ESARROLLO

0.043 0.206



DESARROLLO

D/(D(−)D) ^ E(−)

1.66F 1.054 1-p(x>2) = {p(x=0)Gp(x=1))} 0.132 0.329

a $n $# 80% d$ #! $n$! a #! q'$ $ #$ ap#"ca. $ 7$ ad d$ q'$ $!$n #! c"nc! pac"$n&$. b) La p!bab"#"dad d$ c) :C';n&! pac"$n&$ $ $p$a q'$ $!$n

,AA@LL@ 0.328 (x=3)G(x=4)G(x=5) 0.205 0.410 0.328 0.942 4 . . b"#"dad d$ q'$ c!! 'c*! *aan a#&ad! a &abaa d! p#$ad!

RRROLLO

p(x=0)Gp(x=1)Gp(x=2) 0.015 0.06F 0.143 0.226 'n p!c$! d$ an'ac&'a c!n&"n'a $ 0.06 :C'a#$ !n #a '#! $an d$$c&'!! d$ 'na '$&a a# aa d$ 5 a&"c'#!



0.234 0.030 0.002 0.000 0.000

ada $p$a $&;n a'$n&$ d$# &aba! $n 'n d$&$"nad! 10 &abaad!$ d$ p!d'cc"n paa 'n $&'d"! "'!! d$# a"ab#$ $ d"c$&a ! c!n&"n'a c) d$a!##$ d$ a!##$ 'na d"&"b'c"n ;# $ #a p!bab"#"dad d$ q'$ n"n'n! d$ #! 10 $p#$ad! "a a"ana  d$"ac"n $&;nda d$# d"&"b'c"n.

,AA@LL@ "c$&a. (D(−)D) ^ E(−)

0.35 1 0.95 B095

=

0.9F

Laboratorio sesion 3

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