pareekshanam (probability sidhaantham)

probability sidhaanthathil, ananthamaayi aavarthikkaan kazhiyunnathum sample space ennariyappedunna saadhyamaaya phalangalude oru koottam ullathumaaya eathoru prakriyayumaanu oru pareekshanam allengil trial (chuvade kaanuka). oru pareekshanatthinu onniladhikam saadhyamaaya phalangalundenkil athu "kramarahithamanu" ennum orennam maathrame ulloovenkil athu "nirnnaayakamaan" ennum parayappedunnu. krithyamaayi rund (parasparabandhithamaya) saadhyamaaya falangalulla oru kramarahithamaya pareekshanatthe bernauli trial ennu vilikkunnu.
oru pareekshanam nadathumbol, orennam (onnu maathram) phalangal-eee phalam ethra sambhavangalilum ulppeduthaamenkilum, avayellaam aaa vichaaranayilaan sambhavichathenn parayaam. ore pareekshanatthinte niravadhi pareekshanangal nadathukayum phalangal samaharikkukayum cheytha sesham, oru pareekshanakarthaavinu pareekshanatthil sambhavikkaavunna vividha phalangaludeyum sambhavangaludeyum anubhavaparamaya saadhyathakal vilayiruthaanum sthithivivarakkanakku vishakalana reethikal prayogikkaanum kazhiyum.
pareekshanangalum pareekshanangalum.
koottaaya phalangal sthithivivarakkanakku vishakalanathin vidheyamaakunnathinaayi kramarahithamaya pareekshanangal palappozhum aavarthichu nadathappedunnu. ore pareekshanatthinte oru nischitha ennam aavarthanangal oru samyojitha pareekshanamaayi kanakkakkaam, eee saahacharyathil vyakthigatha aavarthanangale pareekshanangal ennu vilikkunnu. udaaharanathinu, oraal ore nanayam nooru thavana eriyukayum oro phalavum rekhappeduthukayum cheythaal, oro tose nooru tosukal adangiya pareekshanatthinullil oru pareekshanamaayi kanakkakkum.
ganithashaasthra vivaranam.
probability space ennariyappedunna oru ganitha nirmmithiyaan oru kramarahithamaya pareekshanatthe vivarikkukayo maathrkayaakkukayo cheiyunnathu. oru prathyeka tharatthilulla pareekshanamo pareekshanamo manassil vechaanu probability space nirmmikkukayum nirvachikkukayum cheiyunnathu.
oru pareekshanatthinte ganithashaasthra vivaranathil moonnu bhaagangalunda
modalinte orotta nirvvahanatthinte falamaanu oru "phalam". vyakthigatha phalangal praayogikamaayi prayojanappedaathathinaal, phalangalude grouppukale savisheshamaakkaan kooduthal sankeernamaaya "sambhavangal" upayogikkunnu. atharam sambhavangalude shekharam oru "sigma-aljibra" formula _ 1 aanu. avasaanamaayi, oro sambhavathinteyum saadhyatha vyakthamaakkendathundu; ithu "probability alavu" function, "p" upayogichaanu cheiyunnathu.
oru pareekshanam roopakalppana cheyyukayum sthaapikkukayum cheythukazhinjaal, sample spacil ninnu ω, thiranjeduttha phalam adangiyirikkunna formula _ 1 leeii ellah sambhavangalum (oro sambhavavum ω-yude upavibhaagamaanennu oorkkuka) "sambhavichu" ennu parayappedunnu. pareekshanam ananthamaaya ennam thavana aavarthikkukayaanenkil, oro sambhavathinteyum aapekshika aavruthikal avaykku nalkunna moolyangalumaayi yojikkunna reethiyilaan probability function "p" nirvachichirikkunnathu.
oru lalithamaaya pareekshanamenna nilayil, namukk oru nanayam randuthavana thirikkam. sample space (rund flippukalude kramam prasakthamaayirikkumbol) "{(h, t), (t, h), (t, t), (h, h)}" aanu, ivide "h" ennaal "thala" ennum "t" ennaal "vaalukal" ennum ardhamaakkunnu. oronnum "(echu, tii), (tii, echu)", ennu shradhikkuka... pareekshanatthinte saadhyamaaya "phalangal". rund flippukalilum oru "head" sambhavikkumbol sambhavikkunna oru "ivant" namukk nirvachikkaam. eee evantil "(tii, tii)" ozhikeyulla ellah phalangalum adangiyirikkunnu.

