
sub-gassian vitharanam

probability sidhaanthathil, sakthamaaya wall kshayam ulla oru probability vitharanamaanu sub-gausiyan vitharanam. anoupachaarikamaayi, oru sub-gausiyan vitharanathinte vaalukal aadhipathyam pularthunnathu (i.iii. kuranjathu oru gausiyante vaalukal pole vegathil shayikkuka. eee swath sub-gausiyan vitharanagalkk avarude peru nalkunnu. 
aupachaarikamaayi, oro formulakkum positteev sthiraangam "sii" undengil, oru random variable "formula _ 1" nte probability vitharanathe sub-gausiyan ennu vilikkunnu.
sub-gausiyan propertykal.
formula _ 1" oru kramarahithamaya veriyabilaayirikkatte. thaazhepparayunna vyavasthakal thulyamaanu
"thelivu". kekku lair praathinidhyatthinte formula 13, formula 14, formula 15 enna veriyabilukalude maattathinu sesham, aaa formula 16 naam kandethunnu.
formula _ 18: formula _ 19, monodon kanverjans sidhaantham ennivaykkaayi tailor seerees upayogichu formula _ 17 upayogichu, formula _ 22-nuu formula _ 21-nekkaal kuravo thulyamo aaya formula _ 20 namukk labikkum. formula _ 23 edukkuka, thudarnnu formula _ 24 edukkuka.
maarkkovinte asamathwathaal soothravaakyam _ 25, soothravaakyam _ 26
nirvachanangal.
mukalil paranja thulyamaaya vyavasthakalilonnu nilanilkkukayaanenkil oru random variable formula _ 1 neey "sub-gausiyan" random variable ennu vilikkunnu.
formula _ 29 ennu soochippikkunna formula _ 1-nte sub-gausiyan maanadandatthe formula _ 30 ennu nirvachikkunnu, ithu mukalil contition formula _ 33 vazhi oorliks function formula _ 32 srishtikkunna formula _ 1-nte oorliks maanadandamaanu, sub-gausiyan random variabilukale parimithamaaya sub-gausiyan maanadandamulla aaa random veriyabilukalaayi visheshippikkaam.
kooduthal thulyamaaya nirvachanangal.
thaazhepparayunna gunangal thulyamaanu
udaaharanagal.
oru saadhaarana saadhaarana random variable "formula _ 45" oru sub-gausiyan random variablaanu.
formula _ 1" ennathu samamithiyaya bernauli vitharanamulla oru kramarahithamaya veriyabilaayirikkatte. athaayath, "formula _ 1" moolyangalaaya formula _ 48 umm formula _ 49 umm edukkunnu, probability formula _ 50 veetham. formula _ 51" ennathinaal, athu aaa formula _ 52 pinthudarunnu, athinaal "formula _ 1" oru sub-gassian random variablaanu.

