Tarea de Distribucion de Poisson

 

\k`vlrs`ene Nut÷khin el Andn Gnf`bhrk`n Zrhana`f`ene y lstneést`gn

Zrhblshrn Dust`kn Alfli Bfhrls Rlklmns

E`str`aug`hk a`khi`knf Wlilstrl 1:1:-> Wnfvnehr Eurnk Ghrtlz Ilx`gnf` A.G. n inrtls 1? el nar`f elf 1:1:

 

Qlshfvlr fhs s`mu`lktls prhaflins prhpulsths4 >.- Wuphkmnihs qul lf kôilrh el `iplrblgg`hkls lk uk nfniarl elfmneh el gharl s`mul ukn e`str`aug`÷k Zh`sshk ghk ukn ile`n el 1.7 `iplrblgg`hkls phr i`féiltrh. Eltlri`kl fn prhana`f`ene el4 n) 1 `iplrblgg`hkls lk uk i`féiltrh el nfniarl. u91.7 Z(x91) 9 (1.7˅1)(l˅-1.7)/1! 9 :.12?5

a) >: `iplrblgg`hkls lk < i`féiltrhs el nfniarl. u9>.< Z(x9>:) 9 (>>.:)(l˅->>.:! 9 :.>>107<

g) nf ilkhs ukn `iplrblgg`÷k `iplrblgg`÷k lk 1ii el nfniarl. nfniarl. u91*1.7 9 5.2 Z (x≬>) 9 >-Z(x9:) 9>-S(5.2˅:)(l˅-5.2) 9>-S (5.2˅:)(l˅-5.2)/:!Y /:!Y 9 >-:.:>:: 9 :.0?005?

1. 1.-. -. Fn ghkt ghktni ni`k `kng ng`÷ `÷k k ghks ghkst tuy uyl l uk pr prha hafl flin in lk fn bn bnar ar`g `gng ng`÷ `÷k k el e` e`sg sghs hs el nfinglkni`lkth ÷pgh. Lf kôilrh el pnrgufns el ghktni`kng`÷k qul hgurrl lk uk e`sgh ÷pgh lkl ukn e`str`aug`÷k el Zh`sshk y lf kôilrh prhile`h el pnrgufns phr glkiltrh gunerneh el suplrg`l elf e`sgh ls :.>. Lf îrln el uk e`sgh andh lstue`h ls >:: glkiltrhs gunernehs. k9>:: gi˅1 p9:.> pnrgufns/gi˅1 pnrgufns/gi˅1 u 9 kp 9 >:: gi˅1 *:.> pnrgufns/gi˅1 9 >: pnrgufns n) Lkgulktrl fn prhana`f`ene el qul hgurrnk >1 pnrgufns lk lf îrln elf e`sgh andh lstue`h. u9>: Z(x9>1) 9 (>:˅>1)(l˅->:)/>1! 9 :.:0<

a) Fn prhana`f`ene el qul hgurrnk glrh pnrgufns lk lf îrln elf e`sgh andh lstue`h. u9>: Z(x9:) 9 (>:˅:)(l˅->:)/:! 9 :.::::51 h ilkhs pnrgufns hgurrnk lk lf îrln elf e`sgh andh lstue`h. u9>: Z(x≥>1) 9 Z(x9:)+ Z(x9>) + Z(x91) + Z(x97) + Z(x95) + Z(x9:) + Z(x9>>) + Z(x9>1) 9 Z(x≥>1) Z(x≥> 1) 9 (>:˅:)(l˅ (>:˅:)(l˅->:)/: ->:)/:!! + (>:˅>)(l˅-> (>:˅>)(l˅->:)/>! :)/>! + (>:˅1)(l˅ (>:˅1)(l˅->:)/1 ->:)/1!! + (>:˅7)(l˅ (>:˅7)(l˅->:)/ ->:)/7! 7! + (>:˅5)(l˅->:)/5! + (>:˅:)/:˅2)(l˅->:)/2! + (>:˅=)(l˅->:)/=! + (>:˅?)(l˅-

 

>:)/?! + (>:˅0)(l˅->:)/0! + (>:˅>:)(l˅->:)/>:! + (>:˅>>)(l˅->:)/>>! + (>:˅>1)(l˅->:)/>1! 9 :.=0>1 p9?:: u 9 kp 9 (:.:>1)(?::) 9 0.2 Z(x977?) + Z(x91) + Z(x97) + Z(x95) + Z(x9)(l˅-5)/>! 9 :.:=7121- Z(x61) 9 >-SZ(x9:) + Z(x9>) + Z(x91)Y 9 Z(x≬1) 9 >- S(5˅:)(l˅-5)/:! + (5˅>)(l˅-5)/>! + (5˅1)(l˅-5)/1!Y 9 (x≬1) 9 >-:.17?>:77: 9 :.=2>?0220

e) iîs el trls lstàk ghk elblgths Z(x;7) 9 >-Z(x≥7) 9 >‗SZ(x9:) + Z(x9>) + Z(x91) + Z(x97)Y9 Z(x;7) 9 >-:.5775=:> 9 :.1) 9 (:.=1)(l˅-:.=1! 9 :.::::::::::7>17 a) n fh iîs < eurlk ilkhs el uk nþh, Z(x≥) + Z(x91) + Z(x97) + Z(x95) + Z(x9)(l˅-5)/>! 9 :.:=7121<

g) ehs v`hfnk lf g÷e`mh el ghkstrugg`÷k Z(x91) 9 (5˅1)(l˅-5)/1! 9 :.>52- Z(_67) 9 >-SZ(x9:) + Z(x9>) + Z(x91) + Z(x97)Y 9 Z(x≬7) 9 >- S(5˅:)(l˅-5)/:! + (5˅>)(l˅-5)/>! + (5˅1)(l˅-5)/1! + (5˅7)(l˅-5)/7!Y 9 Z(x≬7) 9 >-:.5775=:> 9 :.1:/2: 9 1 Z(x≬7) 9 >- Z(_67) 9 >-SZ(x9:) + Z(x9>) + Z(x91) + Z(x97)Y 9 Z(x≬7) 9 >- S(1˅:)(l˅-1)/:! + (1˅>)(l˅-1)/>! + (1˅1)(l˅-1)/1! + (1˅7)(l˅-1)/7!Y 9 Z(x≬7) 9 >-:.?1752 9 :.>51?=2 >:. Fhs ghgols qul fflmnk n uk slinbhrh s`mulk uk prhglsh el Zh`sshk ghk ile`n el 5 vloľgufhs phr i`kuth. Lf sliîbhrh lstî 5: slmukehs lk rhdh y ?: slmukehs lk vlrel. u9 5*5:/2: 9 1.2 n) ¸Gunf ls fn prhana`f`ene el qul onyn 5 ghgols lk ghfn gunkeh lf slinbhrh slphkl lk vlrel8 Z(x95) 9 (1.2˅5)(l˅-1.2)/5! 9 :.>5>51>

a) ¸Guîf ls fn prhana`f`ene el qul onyn iîs el = ghgols lk ghfn8 Z(x;=) 9 >-Z(x≥=) 9 >‗SZ(x9:) + Z(x9>) + Z(x91) + Z(x97) + Z(x95) + Z(x9-:.005222 9 :.::) 9 >-Z(x6>) 9 >-:.5:.- Fn W`fvnkn \rmlkt Gnrl sl lsplg`nf`zn lk lf gu`eneh el fls`hkls ilkhrls, rlsbr`nens y mr`pl. Lk fns ohrns el fn tnrel el 2->: ZI lf kôilrh ile`h el fflmnens ls 5.: phr ohrn. ¸Guîf ls fn prhana`f`ene el 5 fflmnens lk ukn ohrn8 u95 Z(x95) 9 (5˅5)(l˅-5)/5! 9 :.>01.- Lk uk lxplr`ilkth el fnahrnthr`h, fnahrnthr`h, lf prhile`h el pnrgufns rne`hngvns qul pnsnk phr uk ghktnehr eurnktl > i`f`slmukeh ls el 5. ¸Guîf ls fn prhana`f`ene el qul 2 el fns pnrgufns pnslk phr lf ghktnehr lk uk i`f`slmukeh eneh8 u95 Z(x92) 9 (5˅2)(l˅-5)/2! 9 :.>:5

>7.- Lk g`lrth prhglsh el bnar`gng`÷k lk lf qul sl prheuglk nrgufhs el v`er`h, hgurrlk elblgths h auraudns qul n vlgls elsnghksldnk su vlktn. Wl snal qul lk prhile`h > el gnen >::: nrgufhs prheug`ehs lklk ukn h iîs auraudns. ¸Guîf ls fn prhana`f`ene el qul lk ukn iulstrn nflnthr`n el ?::: sl lkgulktrlk4 k9?::: p9:.::> u9kp9 (?:::)(:.::>) 9 ? n).-ilkhs el = nrgufhs ghk auraudns Z(x6=) 9 Z(x9:) + Z(x9>) + Z(x91) + Z(x97) + Z(x95) + Z(x9)(l˅-?)/>! + (?˅1)(l˅-?)/1! + (?˅7)(l˅-?)/7! + (?˅5)(l˅-?)/5! + (?˅70